内陆水域气-水界面的气体传输:从微电子到超统计

IF 4.6 1区 地球科学 Q2 ENVIRONMENTAL SCIENCES
Gabriel Katul, Andrew Bragg, Ivan Mammarella, Heping Liu, Qi Li, Elie Bou-Zeid
{"title":"内陆水域气-水界面的气体传输:从微电子到超统计","authors":"Gabriel Katul, Andrew Bragg, Ivan Mammarella, Heping Liu, Qi Li, Elie Bou-Zeid","doi":"10.1029/2023wr036615","DOIUrl":null,"url":null,"abstract":"In inland water covering lakes, reservoirs, and ponds, the gas exchange of slightly soluble gases such as carbon dioxide, dimethyl sulfide, methane, or oxygen across a clean and nearly flat air-water interface is routinely described using a water-side mean gas transfer velocity <span data-altimg=\"/cms/asset/d601d164-4c70-4fb9-8cc9-077f60e993c3/wrcr27452-math-0001.png\"></span><mjx-container ctxtmenu_counter=\"533\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" role=\"application\" sre-explorer- style=\"font-size: 103%; position: relative;\" tabindex=\"0\"><mjx-math aria-hidden=\"true\" location=\"graphic/wrcr27452-math-0001.png\"><mjx-semantics><mjx-mrow><mjx-mrow><mjx-mover data-semantic-children=\"2,3\" data-semantic- data-semantic-role=\"latinletter\" data-semantic-speech=\"k Subscript upper L Baseline overbar\" data-semantic-type=\"overscore\"><mjx-over style=\"padding-bottom: 0.105em; margin-bottom: -0.544em;\"><mjx-mo data-semantic- data-semantic-parent=\"4\" data-semantic-role=\"overaccent\" data-semantic-type=\"punctuation\"><mjx-stretchy-h style=\"width: 1.086em;\"><mjx-ext><mjx-c></mjx-c></mjx-ext></mjx-stretchy-h></mjx-mo></mjx-over><mjx-base><mjx-msub data-semantic-children=\"0,1\" data-semantic- data-semantic-parent=\"4\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\" size=\"s\"><mjx-c></mjx-c></mjx-mi></mjx-script></mjx-msub></mjx-base></mjx-mover></mjx-mrow></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml display=\"inline\" unselectable=\"on\"><math altimg=\"urn:x-wiley:00431397:media:wrcr27452:wrcr27452-math-0001\" display=\"inline\" location=\"graphic/wrcr27452-math-0001.png\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><mrow><mover accent=\"true\" data-semantic-=\"\" data-semantic-children=\"2,3\" data-semantic-role=\"latinletter\" data-semantic-speech=\"k Subscript upper L Baseline overbar\" data-semantic-type=\"overscore\"><msub data-semantic-=\"\" data-semantic-children=\"0,1\" data-semantic-parent=\"4\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\"><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"2\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\">k</mi><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"2\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\">L</mi></msub><mo data-semantic-=\"\" data-semantic-parent=\"4\" data-semantic-role=\"overaccent\" data-semantic-type=\"punctuation\">‾</mo></mover></mrow></mrow>$\\overline{{k}_{L}}$</annotation></semantics></math></mjx-assistive-mml></mjx-container>, where overline indicates time or ensemble averaging. The micro-eddy surface renewal model predicts <span data-altimg=\"/cms/asset/f6dd6188-8290-4f30-8ba1-ebf4554d6b5e/wrcr27452-math-0002.png\"></span><mjx-container ctxtmenu_counter=\"534\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" role=\"application\" sre-explorer- style=\"font-size: 103%; position: relative;\" tabindex=\"0\"><mjx-math aria-hidden=\"true\" location=\"graphic/wrcr27452-math-0002.png\"><mjx-semantics><mjx-mrow data-semantic-children=\"4,35\" data-semantic-content=\"5\" data-semantic- data-semantic-role=\"equality\" data-semantic-speech=\"k Subscript upper L Baseline overbar equals alpha Subscript o Baseline upper S c Superscript negative 1 divided by 2 Baseline left parenthesis nu epsilon overbar right parenthesis Superscript 1 divided by 4\" data-semantic-type=\"relseq\"><mjx-mrow><mjx-mover data-semantic-children=\"2,3\" data-semantic- data-semantic-parent=\"36\" data-semantic-role=\"latinletter\" data-semantic-type=\"overscore\"><mjx-over style=\"padding-bottom: 0.105em; margin-bottom: -0.544em;\"><mjx-mo data-semantic- data-semantic-parent=\"4\" data-semantic-role=\"overaccent\" data-semantic-type=\"punctuation\"><mjx-stretchy-h style=\"width: 1.086em;\"><mjx-ext><mjx-c></mjx-c></mjx-ext></mjx-stretchy-h></mjx-mo></mjx-over><mjx-base><mjx-msub data-semantic-children=\"0,1\" data-semantic- data-semantic-parent=\"4\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\" size=\"s\"><mjx-c></mjx-c></mjx-mi></mjx-script></mjx-msub></mjx-base></mjx-mover></mjx-mrow><mjx-mo data-semantic- data-semantic-operator=\"relseq,=\" data-semantic-parent=\"36\" data-semantic-role=\"equality\" data-semantic-type=\"relation\" rspace=\"5\" space=\"5\"><mjx-c></mjx-c></mjx-mo><mjx-mrow data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"8,9,17,31\" data-semantic-content=\"32,33,34\" data-semantic- data-semantic-parent=\"36\" data-semantic-role=\"implicit\" data-semantic-type=\"infixop\"><mjx-msub data-semantic-children=\"6,7\" data-semantic- data-semantic-parent=\"35\" data-semantic-role=\"greekletter\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"8\" data-semantic-role=\"greekletter\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"8\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\" size=\"s\"><mjx-c></mjx-c></mjx-mi></mjx-script></mjx-msub><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,⁢\" data-semantic-parent=\"35\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\" style=\"margin-left: 0.056em; margin-right: 0.056em;\"><mjx-c></mjx-c></mjx-mo><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"35\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,⁢\" data-semantic-parent=\"35\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\" style=\"margin-left: 0.056em; margin-right: 0.056em;\"><mjx-c></mjx-c></mjx-mo><mjx-msup data-semantic-children=\"10,16\" data-semantic- data-semantic-parent=\"35\" data-semantic-role=\"latinletter\" data-semantic-type=\"superscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"17\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi><mjx-script style=\"vertical-align: 0.363em;\"><mjx-mrow data-semantic-children=\"15,14\" data-semantic-content=\"13\" data-semantic- data-semantic-parent=\"17\" data-semantic-role=\"division\" data-semantic-type=\"infixop\" size=\"s\"><mjx-mrow data-semantic-annotation=\"clearspeak:simple\" data-semantic-children=\"12\" data-semantic-content=\"11\" data-semantic- data-semantic-parent=\"16\" data-semantic-role=\"negative\" data-semantic-type=\"prefixop\"><mjx-mo data-semantic- data-semantic-operator=\"prefixop,−\" data-semantic-parent=\"15\" data-semantic-role=\"subtraction\" data-semantic-type=\"operator\" rspace=\"1\"><mjx-c></mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"15\" data-semantic-role=\"integer\" data-semantic-type=\"number\"><mjx-c></mjx-c></mjx-mn></mjx-mrow><mjx-mo data-semantic- data-semantic-operator=\"infixop,/\" data-semantic-parent=\"16\" data-semantic-role=\"division\" data-semantic-type=\"operator\" rspace=\"1\" space=\"1\"><mjx-c></mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"16\" data-semantic-role=\"integer\" data-semantic-type=\"number\"><mjx-c></mjx-c></mjx-mn></mjx-mrow></mjx-script></mjx-msup><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,⁢\" data-semantic-parent=\"35\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\" style=\"margin-left: 0.056em; margin-right: 0.056em;\"><mjx-c></mjx-c></mjx-mo><mjx-msup data-semantic-children=\"26,30\" data-semantic- data-semantic-parent=\"35\" data-semantic-role=\"leftright\" data-semantic-type=\"superscript\"><mjx-mrow data-semantic-children=\"23\" data-semantic-content=\"24,25\" data-semantic- data-semantic-parent=\"31\" data-semantic-role=\"leftright\" data-semantic-type=\"fenced\"><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"fenced\" data-semantic-parent=\"26\" data-semantic-role=\"open\" data-semantic-type=\"fence\" style=\"margin-left: 0.056em; margin-right: 0.056em;\"><mjx-c></mjx-c></mjx-mo><mjx-mrow data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"18,21\" data-semantic-content=\"22\" data-semantic- data-semantic-parent=\"26\" data-semantic-role=\"implicit\" data-semantic-type=\"infixop\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"23\" data-semantic-role=\"greekletter\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,⁢\" data-semantic-parent=\"23\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\" style=\"margin-left: 0.056em; margin-right: 0.056em;\"><mjx-c></mjx-c></mjx-mo><mjx-mover data-semantic-children=\"19,20\" data-semantic- data-semantic-parent=\"23\" data-semantic-role=\"greekletter\" data-semantic-type=\"overscore\"><mjx-over style=\"padding-bottom: 0.105em; padding-left: 0.056em; margin-bottom: -0.544em;\"><mjx-mo data-semantic- data-semantic-parent=\"21\" data-semantic-role=\"overaccent\" data-semantic-type=\"punctuation\"><mjx-c></mjx-c></mjx-mo></mjx-over><mjx-base style=\"padding-left: 0.047em;\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"21\" data-semantic-role=\"greekletter\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi></mjx-base></mjx-mover></mjx-mrow><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"fenced\" data-semantic-parent=\"26\" data-semantic-role=\"close\" data-semantic-type=\"fence\" style=\"margin-left: 0.056em; margin-right: 0.056em;\"><mjx-c></mjx-c></mjx-mo></mjx-mrow><mjx-script style=\"vertical-align: 0.477em;\"><mjx-mrow data-semantic-children=\"27,29\" data-semantic-content=\"28\" data-semantic- data-semantic-parent=\"31\" data-semantic-role=\"division\" data-semantic-type=\"infixop\" size=\"s\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"30\" data-semantic-role=\"integer\" data-semantic-type=\"number\"><mjx-c></mjx-c></mjx-mn><mjx-mo data-semantic- data-semantic-operator=\"infixop,/\" data-semantic-parent=\"30\" data-semantic-role=\"division\" data-semantic-type=\"operator\" rspace=\"1\" space=\"1\"><mjx-c></mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"30\" data-semantic-role=\"integer\" data-semantic-type=\"number\"><mjx-c></mjx-c></mjx-mn></mjx-mrow></mjx-script></mjx-msup></mjx-mrow></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml display=\"inline\" unselectable=\"on\"><math altimg=\"urn:x-wiley:00431397:media:wrcr27452:wrcr27452-math-0002\" display=\"inline\" location=\"graphic/wrcr27452-math-0002.png\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow data-semantic-=\"\" data-semantic-children=\"4,35\" data-semantic-content=\"5\" data-semantic-role=\"equality\" data-semantic-speech=\"k Subscript upper L Baseline overbar equals alpha Subscript o Baseline upper S c Superscript negative 1 divided by 2 Baseline left parenthesis nu epsilon overbar right parenthesis Superscript 1 divided by 4\" data-semantic-type=\"relseq\"><mrow><mover accent=\"true\" data-semantic-=\"\" data-semantic-children=\"2,3\" data-semantic-parent=\"36\" data-semantic-role=\"latinletter\" data-semantic-type=\"overscore\"><msub data-semantic-=\"\" data-semantic-children=\"0,1\" data-semantic-parent=\"4\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\"><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"2\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\">k</mi><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"2\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\">L</mi></msub><mo data-semantic-=\"\" data-semantic-parent=\"4\" data-semantic-role=\"overaccent\" data-semantic-type=\"punctuation\">‾</mo></mover></mrow><mo data-semantic-=\"\" data-semantic-operator=\"relseq,=\" data-semantic-parent=\"36\" data-semantic-role=\"equality\" data-semantic-type=\"relation\">=</mo><mrow data-semantic-=\"\" data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"8,9,17,31\" data-semantic-content=\"32,33,34\" data-semantic-parent=\"36\" data-semantic-role=\"implicit\" data-semantic-type=\"infixop\"><msub data-semantic-=\"\" data-semantic-children=\"6,7\" data-semantic-parent=\"35\" data-semantic-role=\"greekletter\" data-semantic-type=\"subscript\"><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"8\" data-semantic-role=\"greekletter\" data-semantic-type=\"identifier\">α</mi><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"8\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\">o</mi></msub><mo data-semantic-=\"\" data-semantic-added=\"true\" data-semantic-operator=\"infixop,⁢\" data-semantic-parent=\"35\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\">⁢</mo><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"35\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\">S</mi><mo data-semantic-=\"\" data-semantic-added=\"true\" data-semantic-operator=\"infixop,⁢\" data-semantic-parent=\"35\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\">⁢</mo><msup data-semantic-=\"\" data-semantic-children=\"10,16\" data-semantic-parent=\"35\" data-semantic-role=\"latinletter\" data-semantic-type=\"superscript\"><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"17\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\">c</mi><mrow data-semantic-=\"\" data-semantic-children=\"15,14\" data-semantic-content=\"13\" data-semantic-parent=\"17\" data-semantic-role=\"division\" data-semantic-type=\"infixop\"><mrow data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-children=\"12\" data-semantic-content=\"11\" data-semantic-parent=\"16\" data-semantic-role=\"negative\" data-semantic-type=\"prefixop\"><mo data-semantic-=\"\" data-semantic-operator=\"prefixop,−\" data-semantic-parent=\"15\" data-semantic-role=\"subtraction\" data-semantic-type=\"operator\">−</mo><mn data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic-parent=\"15\" data-semantic-role=\"integer\" data-semantic-type=\"number\">1</mn></mrow><mo data-semantic-=\"\" data-semantic-operator=\"infixop,/\" data-semantic-parent=\"16\" data-semantic-role=\"division\" data-semantic-type=\"operator\">/</mo><mn data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic-parent=\"16\" data-semantic-role=\"integer\" data-semantic-type=\"number\">2</mn></mrow></msup><mo data-semantic-=\"\" data-semantic-added=\"true\" data-semantic-operator=\"infixop,⁢\" data-semantic-parent=\"35\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\">⁢</mo><msup data-semantic-=\"\" data-semantic-children=\"26,30\" data-semantic-parent=\"35\" data-semantic-role=\"leftright\" data-semantic-type=\"superscript\"><mrow data-semantic-=\"\" data-semantic-children=\"23\" data-semantic-content=\"24,25\" data-semantic-parent=\"31\" data-semantic-role=\"leftright\" data-semantic-type=\"fenced\"><mo data-semantic-=\"\" data-semantic-added=\"true\" data-semantic-operator=\"fenced\" data-semantic-parent=\"26\" data-semantic-role=\"open\" data-semantic-type=\"fence\">(</mo><mrow data-semantic-=\"\" data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"18,21\" data-semantic-content=\"22\" data-semantic-parent=\"26\" data-semantic-role=\"implicit\" data-semantic-type=\"infixop\"><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"23\" data-semantic-role=\"greekletter\" data-semantic-type=\"identifier\">ν</mi><mo data-semantic-=\"\" data-semantic-added=\"true\" data-semantic-operator=\"infixop,⁢\" data-semantic-parent=\"23\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\">⁢</mo><mover accent=\"true\" data-semantic-=\"\" data-semantic-children=\"19,20\" data-semantic-parent=\"23\" data-semantic-role=\"greekletter\" data-semantic-type=\"overscore\"><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"21\" data-semantic-role=\"greekletter\" data-semantic-type=\"identifier\">ϵ</mi><mo data-semantic-=\"\" data-semantic-parent=\"21\" data-semantic-role=\"overaccent\" data-semantic-type=\"punctuation\">‾</mo></mover></mrow><mo data-semantic-=\"\" data-semantic-added=\"true\" data-semantic-operator=\"fenced\" data-semantic-parent=\"26\" data-semantic-role=\"close\" data-semantic-type=\"fence\">)</mo></mrow><mrow data-semantic-=\"\" data-semantic-children=\"27,29\" data-semantic-content=\"28\" data-semantic-parent=\"31\" data-semantic-role=\"division\" data-semantic-type=\"infixop\"><mn data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic-parent=\"30\" data-semantic-role=\"integer\" data-semantic-type=\"number\">1</mn><mo data-semantic-=\"\" data-semantic-operator=\"infixop,/\" data-semantic-parent=\"30\" data-semantic-role=\"division\" data-semantic-type=\"operator\">/</mo><mn data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic-parent=\"30\" data-semantic-role=\"integer\" data-semantic-type=\"number\">4</mn></mrow></msup></mrow></mrow>$\\overline{{k}_{L}}={\\alpha }_{o}S{c}^{-1/2}{\\left(\\nu \\overline{{\\epsilon}}\\right)}^{1/4}$</annotation></semantics></math></mjx-assistive-mml></mjx-container>, where <span data-altimg=\"/cms/asset/6db4e123-bee9-44a9-91a4-7cf83411b563/wrcr27452-math-0003.png\"></span><mjx-container ctxtmenu_counter=\"535\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" role=\"application\" sre-explorer- style=\"font-size: 103%; position: relative;\" tabindex=\"0\"><mjx-math aria-hidden=\"true\" location=\"graphic/wrcr27452-math-0003.png\"><mjx-semantics><mjx-mrow><mjx-mrow data-semantic-annotation=\"clearspeak:simple;clearspeak:unit\" data-semantic-children=\"0,1\" data-semantic-content=\"2\" data-semantic- data-semantic-role=\"implicit\" data-semantic-speech=\"upper S c\" data-semantic-type=\"infixop\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,⁢\" data-semantic-parent=\"3\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\" style=\"margin-left: 0.056em; margin-right: 0.056em;\"><mjx-c></mjx-c></mjx-mo><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi></mjx-mrow></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml display=\"inline\" unselectable=\"on\"><math altimg=\"urn:x-wiley:00431397:media:wrcr27452:wrcr27452-math-0003\" display=\"inline\" location=\"graphic/wrcr27452-math-0003.png\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><mrow data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple;clearspeak:unit\" data-semantic-children=\"0,1\" data-semantic-content=\"2\" data-semantic-role=\"implicit\" data-semantic-speech=\"upper S c\" data-semantic-type=\"infixop\"><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"3\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\">S</mi><mo data-semantic-=\"\" data-semantic-added=\"true\" data-semantic-operator=\"infixop,⁢\" data-semantic-parent=\"3\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\">⁢</mo><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"3\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\">c</mi></mrow></mrow>$Sc$</annotation></semantics></math></mjx-assistive-mml></mjx-container> is the molecular Schmidt number, <span data-altimg=\"/cms/asset/a75b5e0f-e932-4475-9e0f-ae9f3e36607e/wrcr27452-math-0004.png\"></span><mjx-container ctxtmenu_counter=\"536\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" role=\"application\" sre-explorer- style=\"font-size: 103%; position: relative;\" tabindex=\"0\"><mjx-math aria-hidden=\"true\" location=\"graphic/wrcr27452-math-0004.png\"><mjx-semantics><mjx-mrow><mjx-mrow><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-role=\"greekletter\" data-semantic-speech=\"nu\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi></mjx-mrow></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml display=\"inline\" unselectable=\"on\"><math altimg=\"urn:x-wiley:00431397:media:wrcr27452:wrcr27452-math-0004\" display=\"inline\" location=\"graphic/wrcr27452-math-0004.png\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><mrow><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-role=\"greekletter\" data-semantic-speech=\"nu\" data-semantic-type=\"identifier\">ν</mi></mrow></mrow>$\\nu $</annotation></semantics></math></mjx-assistive-mml></mjx-container> is the water kinematic viscosity, and <span data-altimg=\"/cms/asset/cab18bd3-3709-46ea-8e3e-23a3829c2a80/wrcr27452-math-0005.png\"></span><mjx-container ctxtmenu_counter=\"537\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" role=\"application\" sre-explorer- style=\"font-size: 103%; position: relative;\" tabindex=\"0\"><mjx-math aria-hidden=\"true\" location=\"graphic/wrcr27452-math-0005.png\"><mjx-semantics><mjx-mrow><mjx-mrow><mjx-mover data-semantic-children=\"0,1\" data-semantic- data-semantic-role=\"greekletter\" data-semantic-speech=\"epsilon overbar\" data-semantic-type=\"overscore\"><mjx-over style=\"padding-bottom: 0.105em; padding-left: 0.056em; margin-bottom: -0.544em;\"><mjx-mo data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"overaccent\" data-semantic-type=\"punctuation\"><mjx-c></mjx-c></mjx-mo></mjx-over><mjx-base style=\"padding-left: 0.047em;\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"greekletter\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi></mjx-base></mjx-mover></mjx-mrow></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml display=\"inline\" unselectable=\"on\"><math altimg=\"urn:x-wiley:00431397:media:wrcr27452:wrcr27452-math-0005\" display=\"inline\" location=\"graphic/wrcr27452-math-0005.png\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><mrow><mover accent=\"true\" data-semantic-=\"\" data-semantic-children=\"0,1\" data-semantic-role=\"greekletter\" data-semantic-speech=\"epsilon overbar\" data-semantic-type=\"overscore\"><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"2\" data-semantic-role=\"greekletter\" data-semantic-type=\"identifier\">ϵ</mi><mo data-semantic-=\"\" data-semantic-parent=\"2\" data-semantic-role=\"overaccent\" data-semantic-type=\"punctuation\">‾</mo></mover></mrow></mrow>$\\overline{{\\epsilon}}$</annotation></semantics></math></mjx-assistive-mml></mjx-container> is the waterside mean turbulent kinetic energy dissipation rate at or near the interface. While <span data-altimg=\"/cms/asset/6f1e86dd-1084-41fb-97de-5b44ccfd46dc/wrcr27452-math-0006.png\"></span><mjx-container ctxtmenu_counter=\"538\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" role=\"application\" sre-explorer- style=\"font-size: 103%; position: relative;\" tabindex=\"0\"><mjx-math aria-hidden=\"true\" location=\"graphic/wrcr27452-math-0006.png\"><mjx-semantics><mjx-mrow><mjx-mrow data-semantic-children=\"2,7\" data-semantic-content=\"3\" data-semantic- data-semantic-role=\"equality\" data-semantic-speech=\"alpha Subscript o Baseline equals 0.39 minus 0.46\" data-semantic-type=\"relseq\"><mjx-msub data-semantic-children=\"0,1\" data-semantic- data-semantic-parent=\"8\" data-semantic-role=\"greekletter\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"greekletter\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\" size=\"s\"><mjx-c></mjx-c></mjx-mi></mjx-script></mjx-msub><mjx-mo data-semantic- data-semantic-operator=\"relseq,=\" data-semantic-parent=\"8\" data-semantic-role=\"equality\" data-semantic-type=\"relation\" rspace=\"5\" space=\"5\"><mjx-c></mjx-c></mjx-mo><mjx-mrow data-semantic-children=\"4,6\" data-semantic-content=\"5\" data-semantic- data-semantic-parent=\"8\" data-semantic-role=\"subtraction\" data-semantic-type=\"infixop\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"7\" data-semantic-role=\"float\" data-semantic-type=\"number\"><mjx-c></mjx-c><mjx-c></mjx-c><mjx-c></mjx-c><mjx-c></mjx-c></mjx-mn><mjx-mo data-semantic- data-semantic-operator=\"infixop,−\" data-semantic-parent=\"7\" data-semantic-role=\"subtraction\" data-semantic-type=\"operator\" rspace=\"4\" space=\"4\"><mjx-c></mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"7\" data-semantic-role=\"float\" data-semantic-type=\"number\"><mjx-c></mjx-c><mjx-c></mjx-c><mjx-c></mjx-c><mjx-c></mjx-c></mjx-mn></mjx-mrow></mjx-mrow></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml display=\"inline\" unselectable=\"on\"><math altimg=\"urn:x-wiley:00431397:media:wrcr27452:wrcr27452-math-0006\" display=\"inline\" location=\"graphic/wrcr27452-math-0006.png\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><mrow data-semantic-=\"\" data-semantic-children=\"2,7\" data-semantic-content=\"3\" data-semantic-role=\"equality\" data-semantic-speech=\"alpha Subscript o Baseline equals 0.39 minus 0.46\" data-semantic-type=\"relseq\"><msub data-semantic-=\"\" data-semantic-children=\"0,1\" data-semantic-parent=\"8\" data-semantic-role=\"greekletter\" data-semantic-type=\"subscript\"><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"2\" data-semantic-role=\"greekletter\" data-semantic-type=\"identifier\">α</mi><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"2\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\">o</mi></msub><mo data-semantic-=\"\" data-semantic-operator=\"relseq,=\" data-semantic-parent=\"8\" data-semantic-role=\"equality\" data-semantic-type=\"relation\">=</mo><mrow data-semantic-=\"\" data-semantic-children=\"4,6\" data-semantic-content=\"5\" data-semantic-parent=\"8\" data-semantic-role=\"subtraction\" data-semantic-type=\"infixop\"><mn data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic-parent=\"7\" data-semantic-role=\"float\" data-semantic-type=\"number\">0.39</mn><mo data-semantic-=\"\" data-semantic-operator=\"infixop,−\" data-semantic-parent=\"7\" data-semantic-role=\"subtraction\" data-semantic-type=\"operator\">−</mo><mn data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic-parent=\"7\" data-semantic-role=\"float\" data-semantic-type=\"number\">0.46</mn></mrow></mrow></mrow>${\\alpha }_{o}=0.39-0.46$</annotation></semantics></math></mjx-assistive-mml></mjx-container> has been reported across a number of data sets, others report large scatter or variability around this value range. It is shown here that this scatter can be partly explained by high temporal variability in instantaneous <span data-altimg=\"/cms/asset/9279331e-7f31-4e6c-be38-23075c6e5af7/wrcr27452-math-0007.png\"></span><mjx-container ctxtmenu_counter=\"539\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" role=\"application\" sre-explorer- style=\"font-size: 103%; position: relative;\" tabindex=\"0\"><mjx-math aria-hidden=\"true\" location=\"graphic/wrcr27452-math-0007.png\"><mjx-semantics><mjx-mrow><mjx-mrow><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-role=\"greekletter\" data-semantic-speech=\"epsilon\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi></mjx-mrow></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml display=\"inline\" unselectable=\"on\"><math altimg=\"urn:x-wiley:00431397:media:wrcr27452:wrcr27452-math-0007\" display=\"inline\" location=\"graphic/wrcr27452-math-0007.png\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><mrow><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-role=\"greekletter\" data-semantic-speech=\"epsilon\" data-semantic-type=\"identifier\">ϵ</mi></mrow></mrow>${\\epsilon}$</annotation></semantics></math></mjx-assistive-mml></mjx-container> around <span data-altimg=\"/cms/asset/2695bfeb-19f3-49bc-8a6b-f4b16ed4a970/wrcr27452-math-0008.png\"></span><mjx-container ctxtmenu_counter=\"540\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" role=\"application\" sre-explorer- style=\"font-size: 103%; position: relative;\" tabindex=\"0\"><mjx-math aria-hidden=\"true\" location=\"graphic/wrcr27452-math-0008.png\"><mjx-semantics><mjx-mrow><mjx-mrow><mjx-mover data-semantic-children=\"0,1\" data-semantic- data-semantic-role=\"greekletter\" data-semantic-speech=\"epsilon overbar\" data-semantic-type=\"overscore\"><mjx-over style=\"padding-bottom: 0.105em; padding-left: 0.056em; margin-bottom: -0.544em;\"><mjx-mo data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"overaccent\" data-semantic-type=\"punctuation\"><mjx-c></mjx-c></mjx-mo></mjx-over><mjx-base style=\"padding-left: 0.047em;\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"greekletter\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi></mjx-base></mjx-mover></mjx-mrow></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml display=\"inline\" unselectable=\"on\"><math altimg=\"urn:x-wiley:00431397:media:wrcr27452:wrcr27452-math-0008\" display=\"inline\" location=\"graphic/wrcr27452-math-0008.png\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><mrow><mover accent=\"true\" data-semantic-=\"\" data-semantic-children=\"0,1\" data-semantic-role=\"greekletter\" data-semantic-speech=\"epsilon overbar\" data-semantic-type=\"overscore\"><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"2\" data-semantic-role=\"greekletter\" data-semantic-type=\"identifier\">ϵ</mi><mo data-semantic-=\"\" data-semantic-parent=\"2\" data-semantic-role=\"overaccent\" data-semantic-type=\"punctuation\">‾</mo></mover></mrow></mrow>$\\overline{{\\epsilon}}$</annotation></semantics></math></mjx-assistive-mml></mjx-container>, a mechanism that was not previously considered. As the coefficient of variation <span data-altimg=\"/cms/asset/18ca7845-68e7-4321-8ac7-1a9cacdfc3d1/wrcr27452-math-0009.png\"></span><mjx-container ctxtmenu_counter=\"541\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" role=\"application\" sre-explorer- style=\"font-size: 103%; position: relative;\" tabindex=\"0\"><mjx-math aria-hidden=\"true\" location=\"graphic/wrcr27452-math-0009.png\"><mjx-semantics><mjx-mrow><mjx-mrow><mjx-mrow data-semantic-children=\"5\" data-semantic-content=\"6,7\" data-semantic- data-semantic-role=\"leftright\" data-semantic-speech=\"left parenthesis upper C upper V Subscript e Baseline right parenthesis\" data-semantic-type=\"fenced\"><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"fenced\" data-semantic-parent=\"8\" data-semantic-role=\"open\" data-semantic-type=\"fence\" style=\"margin-left: 0.056em; margin-right: 0.056em;\"><mjx-c></mjx-c></mjx-mo><mjx-mrow data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"0,3\" data-semantic-content=\"4\" data-semantic- data-semantic-parent=\"8\" data-semantic-role=\"implicit\" data-semantic-type=\"infixop\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,⁢\" data-semantic-parent=\"5\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\" style=\"margin-left: 0.056em; margin-right: 0.056em;\"><mjx-c></mjx-c></mjx-mo><mjx-msub data-semantic-children=\"1,2\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em; margin-left: -0.186em;\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\" size=\"s\"><mjx-c></mjx-c></mjx-mi></mjx-script></mjx-msub></mjx-mrow><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"fenced\" data-semantic-parent=\"8\" data-semantic-role=\"close\" data-semantic-type=\"fence\" style=\"margin-left: 0.056em; margin-right: 0.056em;\"><mjx-c></mjx-c></mjx-mo></mjx-mrow></mjx-mrow></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml display=\"inline\" unselectable=\"on\"><math altimg=\"urn:x-wiley:00431397:media:wrcr27452:wrcr27452-math-0009\" display=\"inline\" location=\"graphic/wrcr27452-math-0009.png\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><mrow><mrow data-semantic-=\"\" data-semantic-children=\"5\" data-semantic-content=\"6,7\" data-semantic-role=\"leftright\" data-semantic-speech=\"left parenthesis upper C upper V Subscript e Baseline right parenthesis\" data-semantic-type=\"fenced\"><mo data-semantic-=\"\" data-semantic-added=\"true\" data-semantic-operator=\"fenced\" data-semantic-parent=\"8\" data-semantic-role=\"open\" data-semantic-type=\"fence\">(</mo><mrow data-semantic-=\"\" data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"0,3\" data-semantic-content=\"4\" data-semantic-parent=\"8\" data-semantic-role=\"implicit\" data-semantic-type=\"infixop\"><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\">C</mi><mo data-semantic-=\"\" data-semantic-added=\"true\" data-semantic-operator=\"infixop,⁢\" data-semantic-parent=\"5\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\">⁢</mo><msub data-semantic-=\"\" data-semantic-children=\"1,2\" data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\"><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"3\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\">V</mi><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"3\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\">e</mi></msub></mrow><mo data-semantic-=\"\" data-semantic-added=\"true\" data-semantic-operator=\"fenced\" data-semantic-parent=\"8\" data-semantic-role=\"close\" data-semantic-type=\"fence\">)</mo></mrow></mrow></mrow>$\\left(C{V}_{e}\\right)$</annotation></semantics></math></mjx-assistive-mml></mjx-container> in <span data-altimg=\"/cms/asset/ea4c7838-31fd-4ff2-b22f-95577852ea04/wrcr27452-math-0010.png\"></span><mjx-container ctxtmenu_counter=\"542\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" role=\"application\" sre-explorer- style=\"font-size: 103%; position: relative;\" tabindex=\"0\"><mjx-math aria-hidden=\"true\" location=\"graphic/wrcr27452-math-0010.png\"><mjx-semantics><mjx-mrow><mjx-mrow><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-role=\"greekletter\" data-semantic-speech=\"epsilon\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi></mjx-mrow></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml display=\"inline\" unselectable=\"on\"><math altimg=\"urn:x-wiley:00431397:media:wrcr27452:wrcr27452-math-0010\" display=\"inline\" location=\"graphic/wrcr27452-math-0010.png\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><mrow><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-role=\"greekletter\" data-semantic-speech=\"epsilon\" data-semantic-type=\"identifier\">ϵ</mi></mrow></mrow>${\\epsilon}$</annotation></semantics></math></mjx-assistive-mml></mjx-container> increases, <span data-altimg=\"/cms/asset/160bb215-daee-4d90-b0d6-cd0c6633897c/wrcr27452-math-0011.png\"></span><mjx-container ctxtmenu_counter=\"543\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" role=\"application\" sre-explorer- style=\"font-size: 103%; position: relative;\" tabindex=\"0\"><mjx-math aria-hidden=\"true\" location=\"graphic/wrcr27452-math-0011.png\"><mjx-semantics><mjx-mrow><mjx-mrow><mjx-msub data-semantic-children=\"0,1\" data-semantic- data-semantic-role=\"greekletter\" data-semantic-speech=\"alpha Subscript o\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"greekletter\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\" size=\"s\"><mjx-c></mjx-c></mjx-mi></mjx-script></mjx-msub></mjx-mrow></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml display=\"inline\" unselectable=\"on\"><math altimg=\"urn:x-wiley:00431397:media:wrcr27452:wrcr27452-math-0011\" display=\"inline\" location=\"graphic/wrcr27452-math-0011.png\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><mrow><msub data-semantic-=\"\" data-semantic-children=\"0,1\" data-semantic-role=\"greekletter\" data-semantic-speech=\"alpha Subscript o\" data-semantic-type=\"subscript\"><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"2\" data-semantic-role=\"greekletter\" data-semantic-type=\"identifier\">α</mi><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"2\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\">o</mi></msub></mrow></mrow>${\\alpha }_{o}$</annotation></semantics></math></mjx-assistive-mml></mjx-container> must be adjusted by a multiplier <span data-altimg=\"/cms/asset/6dd1b5ee-6594-457f-847b-0c40dd339a25/wrcr27452-math-0012.png\"></span><mjx-container ctxtmenu_counter=\"544\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" role=\"application\" sre-explorer- style=\"font-size: 103%; position: relative;\" tabindex=\"0\"><mjx-math aria-hidden=\"true\" location=\"graphic/wrcr27452-math-0012.png\"><mjx-semantics><mjx-mrow><mjx-mrow><mjx-msup data-semantic-children=\"13,19\" data-semantic- data-semantic-role=\"leftright\" data-semantic-speech=\"left parenthesis 1 plus upper C upper V Subscript e Superscript 2 Baseline right parenthesis Superscript negative 3 divided by 32\" data-semantic-type=\"superscript\"><mjx-mrow data-semantic-children=\"10\" data-semantic-content=\"11,12\" data-semantic- data-semantic-parent=\"20\" data-semantic-role=\"leftright\" data-semantic-type=\"fenced\"><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"fenced\" data-semantic-parent=\"13\" data-semantic-role=\"open\" data-semantic-type=\"fence\" style=\"margin-left: 0.056em; margin-right: 0.056em;\"><mjx-c></mjx-c></mjx-mo><mjx-mrow data-semantic-children=\"0,9\" data-semantic-content=\"1\" data-semantic- data-semantic-parent=\"13\" data-semantic-role=\"addition\" data-semantic-type=\"infixop\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"10\" data-semantic-role=\"integer\" data-semantic-type=\"number\"><mjx-c></mjx-c></mjx-mn><mjx-mo data-semantic- data-semantic-operator=\"infixop,+\" data-semantic-parent=\"10\" data-semantic-role=\"addition\" data-semantic-type=\"operator\" rspace=\"4\" space=\"4\"><mjx-c></mjx-c></mjx-mo><mjx-mrow data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"2,7\" data-semantic-content=\"8\" data-semantic- data-semantic-parent=\"10\" data-semantic-role=\"implicit\" data-semantic-type=\"infixop\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"9\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,⁢\" data-semantic-parent=\"9\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\" style=\"margin-left: 0.056em; margin-right: 0.056em;\"><mjx-c></mjx-c></mjx-mo><mjx-msubsup data-semantic-children=\"3,4,5\" data-semantic-collapsed=\"(7 (6 3 4) 5)\" data-semantic- data-semantic-parent=\"9\" data-semantic-role=\"latinletter\" data-semantic-type=\"subsup\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"7\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.247em; margin-left: -0.186em;\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"7\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\" style=\"margin-left: 0.347em;\"><mjx-c></mjx-c></mjx-mn><mjx-spacer style=\"margin-top: 0.297em;\"></mjx-spacer><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"7\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\" size=\"s\"><mjx-c></mjx-c></mjx-mi></mjx-script></mjx-msubsup></mjx-mrow></mjx-mrow><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"fenced\" data-semantic-parent=\"13\" data-semantic-role=\"close\" data-semantic-type=\"fence\" style=\"margin-left: 0.056em; margin-right: 0.056em;\"><mjx-c></mjx-c></mjx-mo></mjx-mrow><mjx-script style=\"vertical-align: 0.577em;\"><mjx-mrow data-semantic-children=\"18,17\" data-semantic-content=\"16\" data-semantic- data-semantic-parent=\"20\" data-semantic-role=\"division\" data-semantic-type=\"infixop\" size=\"s\"><mjx-mrow data-semantic-annotation=\"clearspeak:simple\" data-semantic-children=\"15\" data-semantic-content=\"14\" data-semantic- data-semantic-parent=\"19\" data-semantic-role=\"negative\" data-semantic-type=\"prefixop\"><mjx-mo data-semantic- data-semantic-operator=\"prefixop,−\" data-semantic-parent=\"18\" data-semantic-role=\"subtraction\" data-semantic-type=\"operator\" rspace=\"1\"><mjx-c></mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"18\" data-semantic-role=\"integer\" data-semantic-type=\"number\"><mjx-c></mjx-c></mjx-mn></mjx-mrow><mjx-mo data-semantic- data-semantic-operator=\"infixop,/\" data-semantic-parent=\"19\" data-semantic-role=\"division\" data-semantic-type=\"operator\" rspace=\"1\" space=\"1\"><mjx-c></mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"19\" data-semantic-role=\"integer\" data-semantic-type=\"number\"><mjx-c></mjx-c><mjx-c></mjx-c></mjx-mn></mjx-mrow></mjx-script></mjx-msup></mjx-mrow></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml display=\"inline\" unselectable=\"on\"><math altimg=\"urn:x-wiley:00431397:media:wrcr27452:wrcr27452-math-0012\" display=\"inline\" location=\"graphic/wrcr27452-math-0012.png\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><mrow><msup data-semantic-=\"\" data-semantic-children=\"13,19\" data-semantic-role=\"leftright\" data-semantic-speech=\"left parenthesis 1 plus upper C upper V Subscript e Superscript 2 Baseline right parenthesis Superscript negative 3 divided by 32\" data-semantic-type=\"superscript\"><mrow data-semantic-=\"\" data-semantic-children=\"10\" data-semantic-content=\"11,12\" data-semantic-parent=\"20\" data-semantic-role=\"leftright\" data-semantic-type=\"fenced\"><mo data-semantic-=\"\" data-semantic-added=\"true\" data-semantic-operator=\"fenced\" data-semantic-parent=\"13\" data-semantic-role=\"open\" data-semantic-type=\"fence\">(</mo><mrow data-semantic-=\"\" data-semantic-children=\"0,9\" data-semantic-content=\"1\" data-semantic-parent=\"13\" data-semantic-role=\"addition\" data-semantic-type=\"infixop\"><mn data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic-parent=\"10\" data-semantic-role=\"integer\" data-semantic-type=\"number\">1</mn><mo data-semantic-=\"\" data-semantic-operator=\"infixop,+\" data-semantic-parent=\"10\" data-semantic-role=\"addition\" data-semantic-type=\"operator\">+</mo><mrow data-semantic-=\"\" data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"2,7\" data-semantic-content=\"8\" data-semantic-parent=\"10\" data-semantic-role=\"implicit\" data-semantic-type=\"infixop\"><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"9\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\">C</mi><mo data-semantic-=\"\" data-semantic-added=\"true\" data-semantic-operator=\"infixop,⁢\" data-semantic-parent=\"9\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\">⁢</mo><msubsup data-semantic-=\"\" data-semantic-children=\"3,4,5\" data-semantic-collapsed=\"(7 (6 3 4) 5)\" data-semantic-parent=\"9\" data-semantic-role=\"latinletter\" data-semantic-type=\"subsup\"><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"7\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\">V</mi><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"7\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\">e</mi><mn data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic-parent=\"7\" data-semantic-role=\"integer\" data-semantic-type=\"number\">2</mn></msubsup></mrow></mrow><mo data-semantic-=\"\" data-semantic-added=\"true\" data-semantic-operator=\"fenced\" data-semantic-parent=\"13\" data-semantic-role=\"close\" data-semantic-type=\"fence\">)</mo></mrow><mrow data-semantic-=\"\" data-semantic-children=\"18,17\" data-semantic-content=\"16\" data-semantic-parent=\"20\" data-semantic-role=\"division\" data-semantic-type=\"infixop\"><mrow data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-children=\"15\" data-semantic-content=\"14\" data-semantic-parent=\"19\" data-semantic-role=\"negative\" data-semantic-type=\"prefixop\"><mo data-semantic-=\"\" data-semantic-operator=\"prefixop,−\" data-semantic-parent=\"18\" data-semantic-role=\"subtraction\" data-semantic-type=\"operator\">−</mo><mn data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic-parent=\"18\" data-semantic-role=\"integer\" data-semantic-type=\"number\">3</mn></mrow><mo data-semantic-=\"\" data-semantic-operator=\"infixop,/\" data-semantic-parent=\"19\" data-semantic-role=\"division\" data-semantic-type=\"operator\">/</mo><mn data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic-parent=\"19\" data-semantic-role=\"integer\" data-semantic-type=\"number\">32</mn></mrow></msup></mrow></mrow>${\\left(1+C{V}_{e}^{2}\\right)}^{-3/32}$</annotation></semantics></math></mjx-assistive-mml></mjx-container> that was derived from a log-normal model for the probability density function of <span data-altimg=\"/cms/asset/b04fc525-9d9c-4c07-b217-bc318c694fb0/wrcr27452-math-0013.png\"></span><mjx-container ctxtmenu_counter=\"545\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" role=\"application\" sre-explorer- style=\"font-size: 103%; position: relative;\" tabindex=\"0\"><mjx-math aria-hidden=\"true\" location=\"graphic/wrcr27452-math-0013.png\"><mjx-semantics><mjx-mrow><mjx-mrow><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-role=\"greekletter\" data-semantic-speech=\"epsilon\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi></mjx-mrow></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml display=\"inline\" unselectable=\"on\"><math altimg=\"urn:x-wiley:00431397:media:wrcr27452:wrcr27452-math-0013\" display=\"inline\" location=\"graphic/wrcr27452-math-0013.png\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><mrow><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-role=\"greekletter\" data-semantic-speech=\"epsilon\" data-semantic-type=\"identifier\">ϵ</mi></mrow></mrow>${\\epsilon}$</annotation></semantics></math></mjx-assistive-mml></mjx-container>. Reported variations in <span data-altimg=\"/cms/asset/0404188f-f5ed-4b92-a108-2feddeabad08/wrcr27452-math-0014.png\"></span><mjx-container ctxtmenu_counter=\"546\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" role=\"application\" sre-explorer- style=\"font-size: 103%; position: relative;\" tabindex=\"0\"><mjx-math aria-hidden=\"true\" location=\"graphic/wrcr27452-math-0014.png\"><mjx-semantics><mjx-mrow><mjx-mrow><mjx-msub data-semantic-children=\"0,1\" data-semantic- data-semantic-role=\"greekletter\" data-semantic-speech=\"alpha Subscript o\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"greekletter\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\" size=\"s\"><mjx-c></mjx-c></mjx-mi></mjx-script></mjx-msub></mjx-mrow></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml display=\"inline\" unselectable=\"on\"><math altimg=\"urn:x-wiley:00431397:media:wrcr27452:wrcr27452-math-0014\" display=\"inline\" location=\"graphic/wrcr27452-math-0014.png\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><mrow><msub data-semantic-=\"\" data-semantic-children=\"0,1\" data-semantic-role=\"greekletter\" data-semantic-speech=\"alpha Subscript o\" data-semantic-type=\"subscript\"><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"2\" data-semantic-role=\"greekletter\" data-semantic-type=\"identifier\">α</mi><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"2\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\">o</mi></msub></mrow></mrow>${\\alpha }_{o}$</annotation></semantics></math></mjx-assistive-mml></mjx-container> with a macro-scale Reynolds number can also be partly attributed to intermittency effects in <span data-altimg=\"/cms/asset/39e845d6-1bb9-4469-8a67-a3a712c077a2/wrcr27452-math-0015.png\"></span><mjx-container ctxtmenu_counter=\"547\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" role=\"application\" sre-explorer- style=\"font-size: 103%; position: relative;\" tabindex=\"0\"><mjx-math aria-hidden=\"true\" location=\"graphic/wrcr27452-math-0015.png\"><mjx-semantics><mjx-mrow><mjx-mrow><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-role=\"greekletter\" data-semantic-speech=\"epsilon\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi></mjx-mrow></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml display=\"inline\" unselectable=\"on\"><math altimg=\"urn:x-wiley:00431397:media:wrcr27452:wrcr27452-math-0015\" display=\"inline\" location=\"graphic/wrcr27452-math-0015.png\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><mrow><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-role=\"greekletter\" data-semantic-speech=\"epsilon\" data-semantic-type=\"identifier\">ϵ</mi></mrow></mrow>${\\epsilon}$</annotation></semantics></math></mjx-assistive-mml></mjx-container>. Such intermittency is characterized by the long-range (i.e., power-law decay) spatial auto-correlation function of <span data-altimg=\"/cms/asset/f7a7d024-63d4-460d-bb2a-91f89a9ef648/wrcr27452-math-0016.png\"></span><mjx-container ctxtmenu_counter=\"548\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" role=\"application\" sre-explorer- style=\"font-size: 103%; position: relative;\" tabindex=\"0\"><mjx-math aria-hidden=\"true\" location=\"graphic/wrcr27452-math-0016.png\"><mjx-semantics><mjx-mrow><mjx-mrow><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-role=\"greekletter\" data-semantic-speech=\"epsilon\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi></mjx-mrow></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml display=\"inline\" unselectable=\"on\"><math altimg=\"urn:x-wiley:00431397:media:wrcr27452:wrcr27452-math-0016\" display=\"inline\" location=\"graphic/wrcr27452-math-0016.png\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><mrow><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-role=\"greekletter\" data-semantic-speech=\"epsilon\" data-semantic-type=\"identifier\">ϵ</mi></mrow></mrow>${\\epsilon}$</annotation></semantics></math></mjx-assistive-mml></mjx-container>. That <span data-altimg=\"/cms/asset/c0090552-9491-498e-8309-f516233ec033/wrcr27452-math-0017.png\"></span><mjx-container ctxtmenu_counter=\"549\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" role=\"application\" sre-explorer- style=\"font-size: 103%; position: relative;\" tabindex=\"0\"><mjx-math aria-hidden=\"true\" location=\"graphic/wrcr27452-math-0017.png\"><mjx-semantics><mjx-mrow><mjx-mrow><mjx-msub data-semantic-children=\"0,1\" data-semantic- data-semantic-role=\"greekletter\" data-semantic-speech=\"alpha Subscript o\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"greekletter\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\" size=\"s\"><mjx-c></mjx-c></mjx-mi></mjx-script></mjx-msub></mjx-mrow></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml display=\"inline\" unselectable=\"on\"><math altimg=\"urn:x-wiley:00431397:media:wrcr27452:wrcr27452-math-0017\" display=\"inline\" location=\"graphic/wrcr27452-math-0017.png\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><mrow><msub data-semantic-=\"\" data-semantic-children=\"0,1\" data-semantic-role=\"greekletter\" data-semantic-speech=\"alpha Subscript o\" data-semantic-type=\"subscript\"><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"2\" data-semantic-role=\"greekletter\" data-semantic-type=\"identifier\">α</mi><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"2\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\">o</mi></msub></mrow></mrow>${\\alpha }_{o}$</annotation></semantics></math></mjx-assistive-mml></mjx-container> varies with a macro-scale Reynolds number does not necessarily violate the micro-eddy model. Instead, it points to a coordination between the macro- and micro-scales arising from the transfer of energy across scales in the energy cascade.","PeriodicalId":23799,"journal":{"name":"Water Resources Research","volume":"45 1","pages":""},"PeriodicalIF":4.6000,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Gas Transfer Across Air-Water Interfaces in Inland Waters: From Micro-Eddies to Super-Statistics\",\"authors\":\"Gabriel Katul, Andrew Bragg, Ivan Mammarella, Heping Liu, Qi Li, Elie Bou-Zeid\",\"doi\":\"10.1029/2023wr036615\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In inland water covering lakes, reservoirs, and ponds, the gas exchange of slightly soluble gases such as carbon dioxide, dimethyl sulfide, methane, or oxygen across a clean and nearly flat air-water interface is routinely described using a water-side mean gas transfer velocity <span data-altimg=\\\"/cms/asset/d601d164-4c70-4fb9-8cc9-077f60e993c3/wrcr27452-math-0001.png\\\"></span><mjx-container ctxtmenu_counter=\\\"533\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" role=\\\"application\\\" sre-explorer- style=\\\"font-size: 103%; position: relative;\\\" tabindex=\\\"0\\\"><mjx-math aria-hidden=\\\"true\\\" location=\\\"graphic/wrcr27452-math-0001.png\\\"><mjx-semantics><mjx-mrow><mjx-mrow><mjx-mover data-semantic-children=\\\"2,3\\\" data-semantic- data-semantic-role=\\\"latinletter\\\" data-semantic-speech=\\\"k Subscript upper L Baseline overbar\\\" data-semantic-type=\\\"overscore\\\"><mjx-over style=\\\"padding-bottom: 0.105em; margin-bottom: -0.544em;\\\"><mjx-mo data-semantic- data-semantic-parent=\\\"4\\\" data-semantic-role=\\\"overaccent\\\" data-semantic-type=\\\"punctuation\\\"><mjx-stretchy-h style=\\\"width: 1.086em;\\\"><mjx-ext><mjx-c></mjx-c></mjx-ext></mjx-stretchy-h></mjx-mo></mjx-over><mjx-base><mjx-msub data-semantic-children=\\\"0,1\\\" data-semantic- data-semantic-parent=\\\"4\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"subscript\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\"><mjx-c></mjx-c></mjx-mi><mjx-script style=\\\"vertical-align: -0.15em;\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\" size=\\\"s\\\"><mjx-c></mjx-c></mjx-mi></mjx-script></mjx-msub></mjx-base></mjx-mover></mjx-mrow></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml display=\\\"inline\\\" unselectable=\\\"on\\\"><math altimg=\\\"urn:x-wiley:00431397:media:wrcr27452:wrcr27452-math-0001\\\" display=\\\"inline\\\" location=\\\"graphic/wrcr27452-math-0001.png\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><semantics><mrow><mrow><mover accent=\\\"true\\\" data-semantic-=\\\"\\\" data-semantic-children=\\\"2,3\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-speech=\\\"k Subscript upper L Baseline overbar\\\" data-semantic-type=\\\"overscore\\\"><msub data-semantic-=\\\"\\\" data-semantic-children=\\\"0,1\\\" data-semantic-parent=\\\"4\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"subscript\\\"><mi data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\">k</mi><mi data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\">L</mi></msub><mo data-semantic-=\\\"\\\" data-semantic-parent=\\\"4\\\" data-semantic-role=\\\"overaccent\\\" data-semantic-type=\\\"punctuation\\\">‾</mo></mover></mrow></mrow>$\\\\overline{{k}_{L}}$</annotation></semantics></math></mjx-assistive-mml></mjx-container>, where overline indicates time or ensemble averaging. The micro-eddy surface renewal model predicts <span data-altimg=\\\"/cms/asset/f6dd6188-8290-4f30-8ba1-ebf4554d6b5e/wrcr27452-math-0002.png\\\"></span><mjx-container ctxtmenu_counter=\\\"534\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" role=\\\"application\\\" sre-explorer- style=\\\"font-size: 103%; position: relative;\\\" tabindex=\\\"0\\\"><mjx-math aria-hidden=\\\"true\\\" location=\\\"graphic/wrcr27452-math-0002.png\\\"><mjx-semantics><mjx-mrow data-semantic-children=\\\"4,35\\\" data-semantic-content=\\\"5\\\" data-semantic- data-semantic-role=\\\"equality\\\" data-semantic-speech=\\\"k Subscript upper L Baseline overbar equals alpha Subscript o Baseline upper S c Superscript negative 1 divided by 2 Baseline left parenthesis nu epsilon overbar right parenthesis Superscript 1 divided by 4\\\" data-semantic-type=\\\"relseq\\\"><mjx-mrow><mjx-mover data-semantic-children=\\\"2,3\\\" data-semantic- data-semantic-parent=\\\"36\\\" data-semantic-role=\\\"latinletter\\\" 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data-semantic-type=\\\"number\\\"><mjx-c></mjx-c></mjx-mn></mjx-mrow></mjx-script></mjx-msup></mjx-mrow></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml display=\\\"inline\\\" unselectable=\\\"on\\\"><math altimg=\\\"urn:x-wiley:00431397:media:wrcr27452:wrcr27452-math-0002\\\" display=\\\"inline\\\" location=\\\"graphic/wrcr27452-math-0002.png\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><semantics><mrow data-semantic-=\\\"\\\" data-semantic-children=\\\"4,35\\\" data-semantic-content=\\\"5\\\" data-semantic-role=\\\"equality\\\" data-semantic-speech=\\\"k Subscript upper L Baseline overbar equals alpha Subscript o Baseline upper S c Superscript negative 1 divided by 2 Baseline left parenthesis nu epsilon overbar right parenthesis Superscript 1 divided by 4\\\" data-semantic-type=\\\"relseq\\\"><mrow><mover accent=\\\"true\\\" data-semantic-=\\\"\\\" data-semantic-children=\\\"2,3\\\" data-semantic-parent=\\\"36\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"overscore\\\"><msub data-semantic-=\\\"\\\" data-semantic-children=\\\"0,1\\\" data-semantic-parent=\\\"4\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"subscript\\\"><mi data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\">k</mi><mi data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\">L</mi></msub><mo data-semantic-=\\\"\\\" data-semantic-parent=\\\"4\\\" data-semantic-role=\\\"overaccent\\\" data-semantic-type=\\\"punctuation\\\">‾</mo></mover></mrow><mo data-semantic-=\\\"\\\" data-semantic-operator=\\\"relseq,=\\\" data-semantic-parent=\\\"36\\\" data-semantic-role=\\\"equality\\\" data-semantic-type=\\\"relation\\\">=</mo><mrow data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:unit\\\" data-semantic-children=\\\"8,9,17,31\\\" data-semantic-content=\\\"32,33,34\\\" data-semantic-parent=\\\"36\\\" data-semantic-role=\\\"implicit\\\" data-semantic-type=\\\"infixop\\\"><msub data-semantic-=\\\"\\\" data-semantic-children=\\\"6,7\\\" data-semantic-parent=\\\"35\\\" data-semantic-role=\\\"greekletter\\\" data-semantic-type=\\\"subscript\\\"><mi data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic-parent=\\\"8\\\" data-semantic-role=\\\"greekletter\\\" data-semantic-type=\\\"identifier\\\">α</mi><mi data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic-parent=\\\"8\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\">o</mi></msub><mo data-semantic-=\\\"\\\" data-semantic-added=\\\"true\\\" data-semantic-operator=\\\"infixop,⁢\\\" data-semantic-parent=\\\"35\\\" data-semantic-role=\\\"multiplication\\\" data-semantic-type=\\\"operator\\\">⁢</mo><mi data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic-parent=\\\"35\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\">S</mi><mo data-semantic-=\\\"\\\" data-semantic-added=\\\"true\\\" data-semantic-operator=\\\"infixop,⁢\\\" data-semantic-parent=\\\"35\\\" data-semantic-role=\\\"multiplication\\\" data-semantic-type=\\\"operator\\\">⁢</mo><msup data-semantic-=\\\"\\\" data-semantic-children=\\\"10,16\\\" data-semantic-parent=\\\"35\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"superscript\\\"><mi data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic-parent=\\\"17\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\">c</mi><mrow data-semantic-=\\\"\\\" data-semantic-children=\\\"15,14\\\" data-semantic-content=\\\"13\\\" data-semantic-parent=\\\"17\\\" data-semantic-role=\\\"division\\\" data-semantic-type=\\\"infixop\\\"><mrow data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-children=\\\"12\\\" data-semantic-content=\\\"11\\\" data-semantic-parent=\\\"16\\\" data-semantic-role=\\\"negative\\\" data-semantic-type=\\\"prefixop\\\"><mo data-semantic-=\\\"\\\" data-semantic-operator=\\\"prefixop,−\\\" data-semantic-parent=\\\"15\\\" data-semantic-role=\\\"subtraction\\\" data-semantic-type=\\\"operator\\\">−</mo><mn data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic-parent=\\\"15\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\">1</mn></mrow><mo data-semantic-=\\\"\\\" data-semantic-operator=\\\"infixop,/\\\" data-semantic-parent=\\\"16\\\" data-semantic-role=\\\"division\\\" data-semantic-type=\\\"operator\\\">/</mo><mn data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic-parent=\\\"16\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\">2</mn></mrow></msup><mo data-semantic-=\\\"\\\" data-semantic-added=\\\"true\\\" data-semantic-operator=\\\"infixop,⁢\\\" data-semantic-parent=\\\"35\\\" data-semantic-role=\\\"multiplication\\\" data-semantic-type=\\\"operator\\\">⁢</mo><msup data-semantic-=\\\"\\\" data-semantic-children=\\\"26,30\\\" data-semantic-parent=\\\"35\\\" data-semantic-role=\\\"leftright\\\" data-semantic-type=\\\"superscript\\\"><mrow data-semantic-=\\\"\\\" data-semantic-children=\\\"23\\\" data-semantic-content=\\\"24,25\\\" data-semantic-parent=\\\"31\\\" data-semantic-role=\\\"leftright\\\" data-semantic-type=\\\"fenced\\\"><mo data-semantic-=\\\"\\\" data-semantic-added=\\\"true\\\" data-semantic-operator=\\\"fenced\\\" data-semantic-parent=\\\"26\\\" data-semantic-role=\\\"open\\\" data-semantic-type=\\\"fence\\\">(</mo><mrow data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:unit\\\" data-semantic-children=\\\"18,21\\\" data-semantic-content=\\\"22\\\" data-semantic-parent=\\\"26\\\" data-semantic-role=\\\"implicit\\\" data-semantic-type=\\\"infixop\\\"><mi data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic-parent=\\\"23\\\" data-semantic-role=\\\"greekletter\\\" data-semantic-type=\\\"identifier\\\">ν</mi><mo data-semantic-=\\\"\\\" data-semantic-added=\\\"true\\\" data-semantic-operator=\\\"infixop,⁢\\\" data-semantic-parent=\\\"23\\\" data-semantic-role=\\\"multiplication\\\" data-semantic-type=\\\"operator\\\">⁢</mo><mover accent=\\\"true\\\" data-semantic-=\\\"\\\" data-semantic-children=\\\"19,20\\\" data-semantic-parent=\\\"23\\\" data-semantic-role=\\\"greekletter\\\" data-semantic-type=\\\"overscore\\\"><mi data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic-parent=\\\"21\\\" data-semantic-role=\\\"greekletter\\\" data-semantic-type=\\\"identifier\\\">ϵ</mi><mo data-semantic-=\\\"\\\" data-semantic-parent=\\\"21\\\" data-semantic-role=\\\"overaccent\\\" data-semantic-type=\\\"punctuation\\\">‾</mo></mover></mrow><mo data-semantic-=\\\"\\\" data-semantic-added=\\\"true\\\" data-semantic-operator=\\\"fenced\\\" data-semantic-parent=\\\"26\\\" data-semantic-role=\\\"close\\\" data-semantic-type=\\\"fence\\\">)</mo></mrow><mrow data-semantic-=\\\"\\\" data-semantic-children=\\\"27,29\\\" data-semantic-content=\\\"28\\\" data-semantic-parent=\\\"31\\\" data-semantic-role=\\\"division\\\" data-semantic-type=\\\"infixop\\\"><mn data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic-parent=\\\"30\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\">1</mn><mo data-semantic-=\\\"\\\" data-semantic-operator=\\\"infixop,/\\\" data-semantic-parent=\\\"30\\\" data-semantic-role=\\\"division\\\" data-semantic-type=\\\"operator\\\">/</mo><mn data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic-parent=\\\"30\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\">4</mn></mrow></msup></mrow></mrow>$\\\\overline{{k}_{L}}={\\\\alpha }_{o}S{c}^{-1/2}{\\\\left(\\\\nu \\\\overline{{\\\\epsilon}}\\\\right)}^{1/4}$</annotation></semantics></math></mjx-assistive-mml></mjx-container>, where <span data-altimg=\\\"/cms/asset/6db4e123-bee9-44a9-91a4-7cf83411b563/wrcr27452-math-0003.png\\\"></span><mjx-container ctxtmenu_counter=\\\"535\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" role=\\\"application\\\" sre-explorer- style=\\\"font-size: 103%; position: relative;\\\" tabindex=\\\"0\\\"><mjx-math aria-hidden=\\\"true\\\" location=\\\"graphic/wrcr27452-math-0003.png\\\"><mjx-semantics><mjx-mrow><mjx-mrow data-semantic-annotation=\\\"clearspeak:simple;clearspeak:unit\\\" data-semantic-children=\\\"0,1\\\" data-semantic-content=\\\"2\\\" data-semantic- data-semantic-role=\\\"implicit\\\" data-semantic-speech=\\\"upper S c\\\" data-semantic-type=\\\"infixop\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\"><mjx-c></mjx-c></mjx-mi><mjx-mo data-semantic-added=\\\"true\\\" data-semantic- data-semantic-operator=\\\"infixop,⁢\\\" data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"multiplication\\\" data-semantic-type=\\\"operator\\\" style=\\\"margin-left: 0.056em; margin-right: 0.056em;\\\"><mjx-c></mjx-c></mjx-mo><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\"><mjx-c></mjx-c></mjx-mi></mjx-mrow></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml display=\\\"inline\\\" unselectable=\\\"on\\\"><math altimg=\\\"urn:x-wiley:00431397:media:wrcr27452:wrcr27452-math-0003\\\" display=\\\"inline\\\" location=\\\"graphic/wrcr27452-math-0003.png\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><semantics><mrow><mrow data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple;clearspeak:unit\\\" data-semantic-children=\\\"0,1\\\" data-semantic-content=\\\"2\\\" data-semantic-role=\\\"implicit\\\" data-semantic-speech=\\\"upper S c\\\" data-semantic-type=\\\"infixop\\\"><mi data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\">S</mi><mo data-semantic-=\\\"\\\" data-semantic-added=\\\"true\\\" data-semantic-operator=\\\"infixop,⁢\\\" data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"multiplication\\\" data-semantic-type=\\\"operator\\\">⁢</mo><mi data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\">c</mi></mrow></mrow>$Sc$</annotation></semantics></math></mjx-assistive-mml></mjx-container> is the molecular Schmidt number, <span data-altimg=\\\"/cms/asset/a75b5e0f-e932-4475-9e0f-ae9f3e36607e/wrcr27452-math-0004.png\\\"></span><mjx-container ctxtmenu_counter=\\\"536\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" role=\\\"application\\\" sre-explorer- style=\\\"font-size: 103%; position: relative;\\\" tabindex=\\\"0\\\"><mjx-math aria-hidden=\\\"true\\\" location=\\\"graphic/wrcr27452-math-0004.png\\\"><mjx-semantics><mjx-mrow><mjx-mrow><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-role=\\\"greekletter\\\" data-semantic-speech=\\\"nu\\\" data-semantic-type=\\\"identifier\\\"><mjx-c></mjx-c></mjx-mi></mjx-mrow></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml display=\\\"inline\\\" unselectable=\\\"on\\\"><math altimg=\\\"urn:x-wiley:00431397:media:wrcr27452:wrcr27452-math-0004\\\" display=\\\"inline\\\" location=\\\"graphic/wrcr27452-math-0004.png\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><semantics><mrow><mrow><mi data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic-role=\\\"greekletter\\\" data-semantic-speech=\\\"nu\\\" data-semantic-type=\\\"identifier\\\">ν</mi></mrow></mrow>$\\\\nu $</annotation></semantics></math></mjx-assistive-mml></mjx-container> is the water kinematic viscosity, and <span data-altimg=\\\"/cms/asset/cab18bd3-3709-46ea-8e3e-23a3829c2a80/wrcr27452-math-0005.png\\\"></span><mjx-container ctxtmenu_counter=\\\"537\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" role=\\\"application\\\" sre-explorer- style=\\\"font-size: 103%; position: relative;\\\" tabindex=\\\"0\\\"><mjx-math aria-hidden=\\\"true\\\" location=\\\"graphic/wrcr27452-math-0005.png\\\"><mjx-semantics><mjx-mrow><mjx-mrow><mjx-mover data-semantic-children=\\\"0,1\\\" data-semantic- data-semantic-role=\\\"greekletter\\\" data-semantic-speech=\\\"epsilon overbar\\\" data-semantic-type=\\\"overscore\\\"><mjx-over style=\\\"padding-bottom: 0.105em; padding-left: 0.056em; margin-bottom: -0.544em;\\\"><mjx-mo data-semantic- data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"overaccent\\\" data-semantic-type=\\\"punctuation\\\"><mjx-c></mjx-c></mjx-mo></mjx-over><mjx-base style=\\\"padding-left: 0.047em;\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"greekletter\\\" data-semantic-type=\\\"identifier\\\"><mjx-c></mjx-c></mjx-mi></mjx-base></mjx-mover></mjx-mrow></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml display=\\\"inline\\\" unselectable=\\\"on\\\"><math altimg=\\\"urn:x-wiley:00431397:media:wrcr27452:wrcr27452-math-0005\\\" display=\\\"inline\\\" location=\\\"graphic/wrcr27452-math-0005.png\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><semantics><mrow><mrow><mover accent=\\\"true\\\" data-semantic-=\\\"\\\" data-semantic-children=\\\"0,1\\\" data-semantic-role=\\\"greekletter\\\" data-semantic-speech=\\\"epsilon overbar\\\" data-semantic-type=\\\"overscore\\\"><mi data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"greekletter\\\" data-semantic-type=\\\"identifier\\\">ϵ</mi><mo data-semantic-=\\\"\\\" data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"overaccent\\\" data-semantic-type=\\\"punctuation\\\">‾</mo></mover></mrow></mrow>$\\\\overline{{\\\\epsilon}}$</annotation></semantics></math></mjx-assistive-mml></mjx-container> is the waterside mean turbulent kinetic energy dissipation rate at or near the interface. While <span data-altimg=\\\"/cms/asset/6f1e86dd-1084-41fb-97de-5b44ccfd46dc/wrcr27452-math-0006.png\\\"></span><mjx-container ctxtmenu_counter=\\\"538\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" role=\\\"application\\\" sre-explorer- style=\\\"font-size: 103%; position: relative;\\\" tabindex=\\\"0\\\"><mjx-math aria-hidden=\\\"true\\\" location=\\\"graphic/wrcr27452-math-0006.png\\\"><mjx-semantics><mjx-mrow><mjx-mrow data-semantic-children=\\\"2,7\\\" data-semantic-content=\\\"3\\\" data-semantic- data-semantic-role=\\\"equality\\\" data-semantic-speech=\\\"alpha Subscript o Baseline equals 0.39 minus 0.46\\\" data-semantic-type=\\\"relseq\\\"><mjx-msub data-semantic-children=\\\"0,1\\\" data-semantic- data-semantic-parent=\\\"8\\\" data-semantic-role=\\\"greekletter\\\" data-semantic-type=\\\"subscript\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"greekletter\\\" data-semantic-type=\\\"identifier\\\"><mjx-c></mjx-c></mjx-mi><mjx-script style=\\\"vertical-align: -0.15em;\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\" size=\\\"s\\\"><mjx-c></mjx-c></mjx-mi></mjx-script></mjx-msub><mjx-mo data-semantic- data-semantic-operator=\\\"relseq,=\\\" data-semantic-parent=\\\"8\\\" data-semantic-role=\\\"equality\\\" data-semantic-type=\\\"relation\\\" rspace=\\\"5\\\" space=\\\"5\\\"><mjx-c></mjx-c></mjx-mo><mjx-mrow data-semantic-children=\\\"4,6\\\" data-semantic-content=\\\"5\\\" data-semantic- data-semantic-parent=\\\"8\\\" data-semantic-role=\\\"subtraction\\\" data-semantic-type=\\\"infixop\\\"><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"7\\\" data-semantic-role=\\\"float\\\" data-semantic-type=\\\"number\\\"><mjx-c></mjx-c><mjx-c></mjx-c><mjx-c></mjx-c><mjx-c></mjx-c></mjx-mn><mjx-mo data-semantic- data-semantic-operator=\\\"infixop,−\\\" data-semantic-parent=\\\"7\\\" data-semantic-role=\\\"subtraction\\\" data-semantic-type=\\\"operator\\\" rspace=\\\"4\\\" space=\\\"4\\\"><mjx-c></mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"7\\\" data-semantic-role=\\\"float\\\" data-semantic-type=\\\"number\\\"><mjx-c></mjx-c><mjx-c></mjx-c><mjx-c></mjx-c><mjx-c></mjx-c></mjx-mn></mjx-mrow></mjx-mrow></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml display=\\\"inline\\\" unselectable=\\\"on\\\"><math altimg=\\\"urn:x-wiley:00431397:media:wrcr27452:wrcr27452-math-0006\\\" display=\\\"inline\\\" location=\\\"graphic/wrcr27452-math-0006.png\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><semantics><mrow><mrow data-semantic-=\\\"\\\" data-semantic-children=\\\"2,7\\\" data-semantic-content=\\\"3\\\" data-semantic-role=\\\"equality\\\" data-semantic-speech=\\\"alpha Subscript o Baseline equals 0.39 minus 0.46\\\" data-semantic-type=\\\"relseq\\\"><msub data-semantic-=\\\"\\\" data-semantic-children=\\\"0,1\\\" data-semantic-parent=\\\"8\\\" data-semantic-role=\\\"greekletter\\\" data-semantic-type=\\\"subscript\\\"><mi data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"greekletter\\\" data-semantic-type=\\\"identifier\\\">α</mi><mi data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\">o</mi></msub><mo data-semantic-=\\\"\\\" data-semantic-operator=\\\"relseq,=\\\" data-semantic-parent=\\\"8\\\" data-semantic-role=\\\"equality\\\" data-semantic-type=\\\"relation\\\">=</mo><mrow data-semantic-=\\\"\\\" data-semantic-children=\\\"4,6\\\" data-semantic-content=\\\"5\\\" data-semantic-parent=\\\"8\\\" data-semantic-role=\\\"subtraction\\\" data-semantic-type=\\\"infixop\\\"><mn data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic-parent=\\\"7\\\" data-semantic-role=\\\"float\\\" data-semantic-type=\\\"number\\\">0.39</mn><mo data-semantic-=\\\"\\\" data-semantic-operator=\\\"infixop,−\\\" data-semantic-parent=\\\"7\\\" data-semantic-role=\\\"subtraction\\\" data-semantic-type=\\\"operator\\\">−</mo><mn data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic-parent=\\\"7\\\" data-semantic-role=\\\"float\\\" data-semantic-type=\\\"number\\\">0.46</mn></mrow></mrow></mrow>${\\\\alpha }_{o}=0.39-0.46$</annotation></semantics></math></mjx-assistive-mml></mjx-container> has been reported across a number of data sets, others report large scatter or variability around this value range. It is shown here that this scatter can be partly explained by high temporal variability in instantaneous <span data-altimg=\\\"/cms/asset/9279331e-7f31-4e6c-be38-23075c6e5af7/wrcr27452-math-0007.png\\\"></span><mjx-container ctxtmenu_counter=\\\"539\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" role=\\\"application\\\" sre-explorer- style=\\\"font-size: 103%; position: relative;\\\" tabindex=\\\"0\\\"><mjx-math aria-hidden=\\\"true\\\" location=\\\"graphic/wrcr27452-math-0007.png\\\"><mjx-semantics><mjx-mrow><mjx-mrow><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-role=\\\"greekletter\\\" data-semantic-speech=\\\"epsilon\\\" data-semantic-type=\\\"identifier\\\"><mjx-c></mjx-c></mjx-mi></mjx-mrow></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml display=\\\"inline\\\" unselectable=\\\"on\\\"><math altimg=\\\"urn:x-wiley:00431397:media:wrcr27452:wrcr27452-math-0007\\\" display=\\\"inline\\\" location=\\\"graphic/wrcr27452-math-0007.png\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><semantics><mrow><mrow><mi data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic-role=\\\"greekletter\\\" data-semantic-speech=\\\"epsilon\\\" data-semantic-type=\\\"identifier\\\">ϵ</mi></mrow></mrow>${\\\\epsilon}$</annotation></semantics></math></mjx-assistive-mml></mjx-container> around <span data-altimg=\\\"/cms/asset/2695bfeb-19f3-49bc-8a6b-f4b16ed4a970/wrcr27452-math-0008.png\\\"></span><mjx-container ctxtmenu_counter=\\\"540\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" role=\\\"application\\\" sre-explorer- style=\\\"font-size: 103%; position: relative;\\\" tabindex=\\\"0\\\"><mjx-math aria-hidden=\\\"true\\\" location=\\\"graphic/wrcr27452-math-0008.png\\\"><mjx-semantics><mjx-mrow><mjx-mrow><mjx-mover data-semantic-children=\\\"0,1\\\" data-semantic- data-semantic-role=\\\"greekletter\\\" data-semantic-speech=\\\"epsilon overbar\\\" data-semantic-type=\\\"overscore\\\"><mjx-over style=\\\"padding-bottom: 0.105em; padding-left: 0.056em; margin-bottom: -0.544em;\\\"><mjx-mo data-semantic- data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"overaccent\\\" data-semantic-type=\\\"punctuation\\\"><mjx-c></mjx-c></mjx-mo></mjx-over><mjx-base style=\\\"padding-left: 0.047em;\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"greekletter\\\" data-semantic-type=\\\"identifier\\\"><mjx-c></mjx-c></mjx-mi></mjx-base></mjx-mover></mjx-mrow></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml display=\\\"inline\\\" unselectable=\\\"on\\\"><math altimg=\\\"urn:x-wiley:00431397:media:wrcr27452:wrcr27452-math-0008\\\" display=\\\"inline\\\" location=\\\"graphic/wrcr27452-math-0008.png\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><semantics><mrow><mrow><mover accent=\\\"true\\\" data-semantic-=\\\"\\\" data-semantic-children=\\\"0,1\\\" data-semantic-role=\\\"greekletter\\\" data-semantic-speech=\\\"epsilon overbar\\\" data-semantic-type=\\\"overscore\\\"><mi data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"greekletter\\\" data-semantic-type=\\\"identifier\\\">ϵ</mi><mo data-semantic-=\\\"\\\" data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"overaccent\\\" data-semantic-type=\\\"punctuation\\\">‾</mo></mover></mrow></mrow>$\\\\overline{{\\\\epsilon}}$</annotation></semantics></math></mjx-assistive-mml></mjx-container>, a mechanism that was not previously considered. As the coefficient of variation <span data-altimg=\\\"/cms/asset/18ca7845-68e7-4321-8ac7-1a9cacdfc3d1/wrcr27452-math-0009.png\\\"></span><mjx-container ctxtmenu_counter=\\\"541\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" role=\\\"application\\\" sre-explorer- style=\\\"font-size: 103%; position: relative;\\\" tabindex=\\\"0\\\"><mjx-math aria-hidden=\\\"true\\\" location=\\\"graphic/wrcr27452-math-0009.png\\\"><mjx-semantics><mjx-mrow><mjx-mrow><mjx-mrow data-semantic-children=\\\"5\\\" data-semantic-content=\\\"6,7\\\" data-semantic- data-semantic-role=\\\"leftright\\\" data-semantic-speech=\\\"left parenthesis upper C upper V Subscript e Baseline right parenthesis\\\" data-semantic-type=\\\"fenced\\\"><mjx-mo data-semantic-added=\\\"true\\\" data-semantic- data-semantic-operator=\\\"fenced\\\" data-semantic-parent=\\\"8\\\" data-semantic-role=\\\"open\\\" data-semantic-type=\\\"fence\\\" style=\\\"margin-left: 0.056em; margin-right: 0.056em;\\\"><mjx-c></mjx-c></mjx-mo><mjx-mrow data-semantic-annotation=\\\"clearspeak:unit\\\" data-semantic-children=\\\"0,3\\\" data-semantic-content=\\\"4\\\" data-semantic- data-semantic-parent=\\\"8\\\" data-semantic-role=\\\"implicit\\\" data-semantic-type=\\\"infixop\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\"><mjx-c></mjx-c></mjx-mi><mjx-mo data-semantic-added=\\\"true\\\" data-semantic- data-semantic-operator=\\\"infixop,⁢\\\" data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"multiplication\\\" data-semantic-type=\\\"operator\\\" style=\\\"margin-left: 0.056em; margin-right: 0.056em;\\\"><mjx-c></mjx-c></mjx-mo><mjx-msub data-semantic-children=\\\"1,2\\\" data-semantic- data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"subscript\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\"><mjx-c></mjx-c></mjx-mi><mjx-script style=\\\"vertical-align: -0.15em; margin-left: -0.186em;\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\" size=\\\"s\\\"><mjx-c></mjx-c></mjx-mi></mjx-script></mjx-msub></mjx-mrow><mjx-mo data-semantic-added=\\\"true\\\" data-semantic- data-semantic-operator=\\\"fenced\\\" data-semantic-parent=\\\"8\\\" data-semantic-role=\\\"close\\\" data-semantic-type=\\\"fence\\\" style=\\\"margin-left: 0.056em; margin-right: 0.056em;\\\"><mjx-c></mjx-c></mjx-mo></mjx-mrow></mjx-mrow></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml display=\\\"inline\\\" unselectable=\\\"on\\\"><math altimg=\\\"urn:x-wiley:00431397:media:wrcr27452:wrcr27452-math-0009\\\" display=\\\"inline\\\" location=\\\"graphic/wrcr27452-math-0009.png\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><semantics><mrow><mrow><mrow data-semantic-=\\\"\\\" data-semantic-children=\\\"5\\\" data-semantic-content=\\\"6,7\\\" data-semantic-role=\\\"leftright\\\" data-semantic-speech=\\\"left parenthesis upper C upper V Subscript e Baseline right parenthesis\\\" data-semantic-type=\\\"fenced\\\"><mo data-semantic-=\\\"\\\" data-semantic-added=\\\"true\\\" data-semantic-operator=\\\"fenced\\\" data-semantic-parent=\\\"8\\\" data-semantic-role=\\\"open\\\" data-semantic-type=\\\"fence\\\">(</mo><mrow data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:unit\\\" data-semantic-children=\\\"0,3\\\" data-semantic-content=\\\"4\\\" data-semantic-parent=\\\"8\\\" data-semantic-role=\\\"implicit\\\" data-semantic-type=\\\"infixop\\\"><mi data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\">C</mi><mo data-semantic-=\\\"\\\" data-semantic-added=\\\"true\\\" data-semantic-operator=\\\"infixop,⁢\\\" data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"multiplication\\\" data-semantic-type=\\\"operator\\\">⁢</mo><msub data-semantic-=\\\"\\\" data-semantic-children=\\\"1,2\\\" data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"subscript\\\"><mi data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\">V</mi><mi data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\">e</mi></msub></mrow><mo data-semantic-=\\\"\\\" data-semantic-added=\\\"true\\\" data-semantic-operator=\\\"fenced\\\" data-semantic-parent=\\\"8\\\" data-semantic-role=\\\"close\\\" data-semantic-type=\\\"fence\\\">)</mo></mrow></mrow></mrow>$\\\\left(C{V}_{e}\\\\right)$</annotation></semantics></math></mjx-assistive-mml></mjx-container> in <span data-altimg=\\\"/cms/asset/ea4c7838-31fd-4ff2-b22f-95577852ea04/wrcr27452-math-0010.png\\\"></span><mjx-container ctxtmenu_counter=\\\"542\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" role=\\\"application\\\" sre-explorer- style=\\\"font-size: 103%; position: relative;\\\" tabindex=\\\"0\\\"><mjx-math aria-hidden=\\\"true\\\" location=\\\"graphic/wrcr27452-math-0010.png\\\"><mjx-semantics><mjx-mrow><mjx-mrow><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-role=\\\"greekletter\\\" data-semantic-speech=\\\"epsilon\\\" data-semantic-type=\\\"identifier\\\"><mjx-c></mjx-c></mjx-mi></mjx-mrow></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml display=\\\"inline\\\" unselectable=\\\"on\\\"><math altimg=\\\"urn:x-wiley:00431397:media:wrcr27452:wrcr27452-math-0010\\\" display=\\\"inline\\\" location=\\\"graphic/wrcr27452-math-0010.png\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><semantics><mrow><mrow><mi data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic-role=\\\"greekletter\\\" data-semantic-speech=\\\"epsilon\\\" data-semantic-type=\\\"identifier\\\">ϵ</mi></mrow></mrow>${\\\\epsilon}$</annotation></semantics></math></mjx-assistive-mml></mjx-container> increases, <span data-altimg=\\\"/cms/asset/160bb215-daee-4d90-b0d6-cd0c6633897c/wrcr27452-math-0011.png\\\"></span><mjx-container ctxtmenu_counter=\\\"543\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" role=\\\"application\\\" sre-explorer- style=\\\"font-size: 103%; position: relative;\\\" tabindex=\\\"0\\\"><mjx-math aria-hidden=\\\"true\\\" location=\\\"graphic/wrcr27452-math-0011.png\\\"><mjx-semantics><mjx-mrow><mjx-mrow><mjx-msub data-semantic-children=\\\"0,1\\\" data-semantic- data-semantic-role=\\\"greekletter\\\" data-semantic-speech=\\\"alpha Subscript o\\\" data-semantic-type=\\\"subscript\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"greekletter\\\" data-semantic-type=\\\"identifier\\\"><mjx-c></mjx-c></mjx-mi><mjx-script style=\\\"vertical-align: -0.15em;\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\" size=\\\"s\\\"><mjx-c></mjx-c></mjx-mi></mjx-script></mjx-msub></mjx-mrow></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml display=\\\"inline\\\" unselectable=\\\"on\\\"><math altimg=\\\"urn:x-wiley:00431397:media:wrcr27452:wrcr27452-math-0011\\\" display=\\\"inline\\\" location=\\\"graphic/wrcr27452-math-0011.png\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><semantics><mrow><mrow><msub data-semantic-=\\\"\\\" data-semantic-children=\\\"0,1\\\" data-semantic-role=\\\"greekletter\\\" data-semantic-speech=\\\"alpha Subscript o\\\" data-semantic-type=\\\"subscript\\\"><mi data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"greekletter\\\" data-semantic-type=\\\"identifier\\\">α</mi><mi data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\">o</mi></msub></mrow></mrow>${\\\\alpha }_{o}$</annotation></semantics></math></mjx-assistive-mml></mjx-container> must be adjusted by a multiplier <span data-altimg=\\\"/cms/asset/6dd1b5ee-6594-457f-847b-0c40dd339a25/wrcr27452-math-0012.png\\\"></span><mjx-container ctxtmenu_counter=\\\"544\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" role=\\\"application\\\" sre-explorer- style=\\\"font-size: 103%; position: relative;\\\" tabindex=\\\"0\\\"><mjx-math aria-hidden=\\\"true\\\" location=\\\"graphic/wrcr27452-math-0012.png\\\"><mjx-semantics><mjx-mrow><mjx-mrow><mjx-msup data-semantic-children=\\\"13,19\\\" data-semantic- data-semantic-role=\\\"leftright\\\" data-semantic-speech=\\\"left parenthesis 1 plus upper C upper V Subscript e Superscript 2 Baseline right parenthesis Superscript negative 3 divided by 32\\\" data-semantic-type=\\\"superscript\\\"><mjx-mrow data-semantic-children=\\\"10\\\" data-semantic-content=\\\"11,12\\\" data-semantic- data-semantic-parent=\\\"20\\\" data-semantic-role=\\\"leftright\\\" data-semantic-type=\\\"fenced\\\"><mjx-mo data-semantic-added=\\\"true\\\" data-semantic- data-semantic-operator=\\\"fenced\\\" data-semantic-parent=\\\"13\\\" data-semantic-role=\\\"open\\\" data-semantic-type=\\\"fence\\\" style=\\\"margin-left: 0.056em; margin-right: 0.056em;\\\"><mjx-c></mjx-c></mjx-mo><mjx-mrow data-semantic-children=\\\"0,9\\\" data-semantic-content=\\\"1\\\" data-semantic- data-semantic-parent=\\\"13\\\" data-semantic-role=\\\"addition\\\" data-semantic-type=\\\"infixop\\\"><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"10\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\"><mjx-c></mjx-c></mjx-mn><mjx-mo data-semantic- data-semantic-operator=\\\"infixop,+\\\" data-semantic-parent=\\\"10\\\" data-semantic-role=\\\"addition\\\" data-semantic-type=\\\"operator\\\" rspace=\\\"4\\\" space=\\\"4\\\"><mjx-c></mjx-c></mjx-mo><mjx-mrow data-semantic-annotation=\\\"clearspeak:unit\\\" data-semantic-children=\\\"2,7\\\" data-semantic-content=\\\"8\\\" data-semantic- data-semantic-parent=\\\"10\\\" data-semantic-role=\\\"implicit\\\" data-semantic-type=\\\"infixop\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"9\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\"><mjx-c></mjx-c></mjx-mi><mjx-mo data-semantic-added=\\\"true\\\" data-semantic- data-semantic-operator=\\\"infixop,⁢\\\" data-semantic-parent=\\\"9\\\" data-semantic-role=\\\"multiplication\\\" data-semantic-type=\\\"operator\\\" style=\\\"margin-left: 0.056em; margin-right: 0.056em;\\\"><mjx-c></mjx-c></mjx-mo><mjx-msubsup data-semantic-children=\\\"3,4,5\\\" data-semantic-collapsed=\\\"(7 (6 3 4) 5)\\\" data-semantic- data-semantic-parent=\\\"9\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"subsup\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"7\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\"><mjx-c></mjx-c></mjx-mi><mjx-script style=\\\"vertical-align: -0.247em; margin-left: -0.186em;\\\"><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"7\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\" size=\\\"s\\\" style=\\\"margin-left: 0.347em;\\\"><mjx-c></mjx-c></mjx-mn><mjx-spacer style=\\\"margin-top: 0.297em;\\\"></mjx-spacer><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"7\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\" size=\\\"s\\\"><mjx-c></mjx-c></mjx-mi></mjx-script></mjx-msubsup></mjx-mrow></mjx-mrow><mjx-mo data-semantic-added=\\\"true\\\" data-semantic- data-semantic-operator=\\\"fenced\\\" data-semantic-parent=\\\"13\\\" data-semantic-role=\\\"close\\\" data-semantic-type=\\\"fence\\\" style=\\\"margin-left: 0.056em; margin-right: 0.056em;\\\"><mjx-c></mjx-c></mjx-mo></mjx-mrow><mjx-script style=\\\"vertical-align: 0.577em;\\\"><mjx-mrow data-semantic-children=\\\"18,17\\\" data-semantic-content=\\\"16\\\" data-semantic- data-semantic-parent=\\\"20\\\" data-semantic-role=\\\"division\\\" data-semantic-type=\\\"infixop\\\" size=\\\"s\\\"><mjx-mrow data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-children=\\\"15\\\" data-semantic-content=\\\"14\\\" data-semantic- data-semantic-parent=\\\"19\\\" data-semantic-role=\\\"negative\\\" data-semantic-type=\\\"prefixop\\\"><mjx-mo data-semantic- data-semantic-operator=\\\"prefixop,−\\\" data-semantic-parent=\\\"18\\\" data-semantic-role=\\\"subtraction\\\" data-semantic-type=\\\"operator\\\" rspace=\\\"1\\\"><mjx-c></mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"18\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\"><mjx-c></mjx-c></mjx-mn></mjx-mrow><mjx-mo data-semantic- data-semantic-operator=\\\"infixop,/\\\" data-semantic-parent=\\\"19\\\" data-semantic-role=\\\"division\\\" data-semantic-type=\\\"operator\\\" rspace=\\\"1\\\" space=\\\"1\\\"><mjx-c></mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"19\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\"><mjx-c></mjx-c><mjx-c></mjx-c></mjx-mn></mjx-mrow></mjx-script></mjx-msup></mjx-mrow></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml display=\\\"inline\\\" unselectable=\\\"on\\\"><math altimg=\\\"urn:x-wiley:00431397:media:wrcr27452:wrcr27452-math-0012\\\" display=\\\"inline\\\" location=\\\"graphic/wrcr27452-math-0012.png\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><semantics><mrow><mrow><msup data-semantic-=\\\"\\\" data-semantic-children=\\\"13,19\\\" data-semantic-role=\\\"leftright\\\" data-semantic-speech=\\\"left parenthesis 1 plus upper C upper V Subscript e Superscript 2 Baseline right parenthesis Superscript negative 3 divided by 32\\\" data-semantic-type=\\\"superscript\\\"><mrow data-semantic-=\\\"\\\" data-semantic-children=\\\"10\\\" data-semantic-content=\\\"11,12\\\" data-semantic-parent=\\\"20\\\" data-semantic-role=\\\"leftright\\\" data-semantic-type=\\\"fenced\\\"><mo data-semantic-=\\\"\\\" data-semantic-added=\\\"true\\\" data-semantic-operator=\\\"fenced\\\" data-semantic-parent=\\\"13\\\" data-semantic-role=\\\"open\\\" data-semantic-type=\\\"fence\\\">(</mo><mrow data-semantic-=\\\"\\\" data-semantic-children=\\\"0,9\\\" data-semantic-content=\\\"1\\\" data-semantic-parent=\\\"13\\\" data-semantic-role=\\\"addition\\\" data-semantic-type=\\\"infixop\\\"><mn data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic-parent=\\\"10\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\">1</mn><mo data-semantic-=\\\"\\\" data-semantic-operator=\\\"infixop,+\\\" data-semantic-parent=\\\"10\\\" data-semantic-role=\\\"addition\\\" data-semantic-type=\\\"operator\\\">+</mo><mrow data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:unit\\\" data-semantic-children=\\\"2,7\\\" data-semantic-content=\\\"8\\\" data-semantic-parent=\\\"10\\\" data-semantic-role=\\\"implicit\\\" data-semantic-type=\\\"infixop\\\"><mi data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic-parent=\\\"9\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\">C</mi><mo data-semantic-=\\\"\\\" data-semantic-added=\\\"true\\\" data-semantic-operator=\\\"infixop,⁢\\\" data-semantic-parent=\\\"9\\\" data-semantic-role=\\\"multiplication\\\" data-semantic-type=\\\"operator\\\">⁢</mo><msubsup data-semantic-=\\\"\\\" data-semantic-children=\\\"3,4,5\\\" data-semantic-collapsed=\\\"(7 (6 3 4) 5)\\\" data-semantic-parent=\\\"9\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"subsup\\\"><mi data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic-parent=\\\"7\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\">V</mi><mi data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic-parent=\\\"7\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\">e</mi><mn data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic-parent=\\\"7\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\">2</mn></msubsup></mrow></mrow><mo data-semantic-=\\\"\\\" data-semantic-added=\\\"true\\\" data-semantic-operator=\\\"fenced\\\" data-semantic-parent=\\\"13\\\" data-semantic-role=\\\"close\\\" data-semantic-type=\\\"fence\\\">)</mo></mrow><mrow data-semantic-=\\\"\\\" data-semantic-children=\\\"18,17\\\" data-semantic-content=\\\"16\\\" data-semantic-parent=\\\"20\\\" data-semantic-role=\\\"division\\\" data-semantic-type=\\\"infixop\\\"><mrow data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-children=\\\"15\\\" data-semantic-content=\\\"14\\\" data-semantic-parent=\\\"19\\\" data-semantic-role=\\\"negative\\\" data-semantic-type=\\\"prefixop\\\"><mo data-semantic-=\\\"\\\" data-semantic-operator=\\\"prefixop,−\\\" data-semantic-parent=\\\"18\\\" data-semantic-role=\\\"subtraction\\\" data-semantic-type=\\\"operator\\\">−</mo><mn data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic-parent=\\\"18\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\">3</mn></mrow><mo data-semantic-=\\\"\\\" data-semantic-operator=\\\"infixop,/\\\" data-semantic-parent=\\\"19\\\" data-semantic-role=\\\"division\\\" data-semantic-type=\\\"operator\\\">/</mo><mn data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic-parent=\\\"19\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\">32</mn></mrow></msup></mrow></mrow>${\\\\left(1+C{V}_{e}^{2}\\\\right)}^{-3/32}$</annotation></semantics></math></mjx-assistive-mml></mjx-container> that was derived from a log-normal model for the probability density function of <span data-altimg=\\\"/cms/asset/b04fc525-9d9c-4c07-b217-bc318c694fb0/wrcr27452-math-0013.png\\\"></span><mjx-container ctxtmenu_counter=\\\"545\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" role=\\\"application\\\" sre-explorer- style=\\\"font-size: 103%; position: relative;\\\" tabindex=\\\"0\\\"><mjx-math aria-hidden=\\\"true\\\" location=\\\"graphic/wrcr27452-math-0013.png\\\"><mjx-semantics><mjx-mrow><mjx-mrow><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-role=\\\"greekletter\\\" data-semantic-speech=\\\"epsilon\\\" data-semantic-type=\\\"identifier\\\"><mjx-c></mjx-c></mjx-mi></mjx-mrow></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml display=\\\"inline\\\" unselectable=\\\"on\\\"><math altimg=\\\"urn:x-wiley:00431397:media:wrcr27452:wrcr27452-math-0013\\\" display=\\\"inline\\\" location=\\\"graphic/wrcr27452-math-0013.png\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><semantics><mrow><mrow><mi data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic-role=\\\"greekletter\\\" data-semantic-speech=\\\"epsilon\\\" data-semantic-type=\\\"identifier\\\">ϵ</mi></mrow></mrow>${\\\\epsilon}$</annotation></semantics></math></mjx-assistive-mml></mjx-container>. Reported variations in <span data-altimg=\\\"/cms/asset/0404188f-f5ed-4b92-a108-2feddeabad08/wrcr27452-math-0014.png\\\"></span><mjx-container ctxtmenu_counter=\\\"546\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" role=\\\"application\\\" sre-explorer- style=\\\"font-size: 103%; position: relative;\\\" tabindex=\\\"0\\\"><mjx-math aria-hidden=\\\"true\\\" location=\\\"graphic/wrcr27452-math-0014.png\\\"><mjx-semantics><mjx-mrow><mjx-mrow><mjx-msub data-semantic-children=\\\"0,1\\\" data-semantic- data-semantic-role=\\\"greekletter\\\" data-semantic-speech=\\\"alpha Subscript o\\\" data-semantic-type=\\\"subscript\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"greekletter\\\" data-semantic-type=\\\"identifier\\\"><mjx-c></mjx-c></mjx-mi><mjx-script style=\\\"vertical-align: -0.15em;\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\" size=\\\"s\\\"><mjx-c></mjx-c></mjx-mi></mjx-script></mjx-msub></mjx-mrow></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml display=\\\"inline\\\" unselectable=\\\"on\\\"><math altimg=\\\"urn:x-wiley:00431397:media:wrcr27452:wrcr27452-math-0014\\\" display=\\\"inline\\\" location=\\\"graphic/wrcr27452-math-0014.png\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><semantics><mrow><mrow><msub data-semantic-=\\\"\\\" data-semantic-children=\\\"0,1\\\" data-semantic-role=\\\"greekletter\\\" data-semantic-speech=\\\"alpha Subscript o\\\" data-semantic-type=\\\"subscript\\\"><mi data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"greekletter\\\" data-semantic-type=\\\"identifier\\\">α</mi><mi data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\">o</mi></msub></mrow></mrow>${\\\\alpha }_{o}$</annotation></semantics></math></mjx-assistive-mml></mjx-container> with a macro-scale Reynolds number can also be partly attributed to intermittency effects in <span data-altimg=\\\"/cms/asset/39e845d6-1bb9-4469-8a67-a3a712c077a2/wrcr27452-math-0015.png\\\"></span><mjx-container ctxtmenu_counter=\\\"547\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" role=\\\"application\\\" sre-explorer- style=\\\"font-size: 103%; position: relative;\\\" tabindex=\\\"0\\\"><mjx-math aria-hidden=\\\"true\\\" location=\\\"graphic/wrcr27452-math-0015.png\\\"><mjx-semantics><mjx-mrow><mjx-mrow><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-role=\\\"greekletter\\\" data-semantic-speech=\\\"epsilon\\\" data-semantic-type=\\\"identifier\\\"><mjx-c></mjx-c></mjx-mi></mjx-mrow></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml display=\\\"inline\\\" unselectable=\\\"on\\\"><math altimg=\\\"urn:x-wiley:00431397:media:wrcr27452:wrcr27452-math-0015\\\" display=\\\"inline\\\" location=\\\"graphic/wrcr27452-math-0015.png\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><semantics><mrow><mrow><mi data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic-role=\\\"greekletter\\\" data-semantic-speech=\\\"epsilon\\\" data-semantic-type=\\\"identifier\\\">ϵ</mi></mrow></mrow>${\\\\epsilon}$</annotation></semantics></math></mjx-assistive-mml></mjx-container>. Such intermittency is characterized by the long-range (i.e., power-law decay) spatial auto-correlation function of <span data-altimg=\\\"/cms/asset/f7a7d024-63d4-460d-bb2a-91f89a9ef648/wrcr27452-math-0016.png\\\"></span><mjx-container ctxtmenu_counter=\\\"548\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" role=\\\"application\\\" sre-explorer- style=\\\"font-size: 103%; position: relative;\\\" tabindex=\\\"0\\\"><mjx-math aria-hidden=\\\"true\\\" location=\\\"graphic/wrcr27452-math-0016.png\\\"><mjx-semantics><mjx-mrow><mjx-mrow><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-role=\\\"greekletter\\\" data-semantic-speech=\\\"epsilon\\\" data-semantic-type=\\\"identifier\\\"><mjx-c></mjx-c></mjx-mi></mjx-mrow></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml display=\\\"inline\\\" unselectable=\\\"on\\\"><math altimg=\\\"urn:x-wiley:00431397:media:wrcr27452:wrcr27452-math-0016\\\" display=\\\"inline\\\" location=\\\"graphic/wrcr27452-math-0016.png\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><semantics><mrow><mrow><mi data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic-role=\\\"greekletter\\\" data-semantic-speech=\\\"epsilon\\\" data-semantic-type=\\\"identifier\\\">ϵ</mi></mrow></mrow>${\\\\epsilon}$</annotation></semantics></math></mjx-assistive-mml></mjx-container>. That <span data-altimg=\\\"/cms/asset/c0090552-9491-498e-8309-f516233ec033/wrcr27452-math-0017.png\\\"></span><mjx-container ctxtmenu_counter=\\\"549\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" role=\\\"application\\\" sre-explorer- style=\\\"font-size: 103%; position: relative;\\\" tabindex=\\\"0\\\"><mjx-math aria-hidden=\\\"true\\\" location=\\\"graphic/wrcr27452-math-0017.png\\\"><mjx-semantics><mjx-mrow><mjx-mrow><mjx-msub data-semantic-children=\\\"0,1\\\" data-semantic- data-semantic-role=\\\"greekletter\\\" data-semantic-speech=\\\"alpha Subscript o\\\" data-semantic-type=\\\"subscript\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"greekletter\\\" data-semantic-type=\\\"identifier\\\"><mjx-c></mjx-c></mjx-mi><mjx-script style=\\\"vertical-align: -0.15em;\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\" size=\\\"s\\\"><mjx-c></mjx-c></mjx-mi></mjx-script></mjx-msub></mjx-mrow></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml display=\\\"inline\\\" unselectable=\\\"on\\\"><math altimg=\\\"urn:x-wiley:00431397:media:wrcr27452:wrcr27452-math-0017\\\" display=\\\"inline\\\" location=\\\"graphic/wrcr27452-math-0017.png\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><semantics><mrow><mrow><msub data-semantic-=\\\"\\\" data-semantic-children=\\\"0,1\\\" data-semantic-role=\\\"greekletter\\\" data-semantic-speech=\\\"alpha Subscript o\\\" data-semantic-type=\\\"subscript\\\"><mi data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"greekletter\\\" data-semantic-type=\\\"identifier\\\">α</mi><mi data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\">o</mi></msub></mrow></mrow>${\\\\alpha }_{o}$</annotation></semantics></math></mjx-assistive-mml></mjx-container> varies with a macro-scale Reynolds number does not necessarily violate the micro-eddy model. 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引用次数: 0

摘要

在覆盖湖泊、水库和池塘的内陆水域中,二氧化碳、二甲基硫化物、甲烷或氧气等微溶性气体在清洁且近乎平坦的空气-水界面上的气体交换通常使用水侧平均气体传输速度 kL‾$/overline{{k}_{L}}$ 来描述,其中 overline 表示时间或集合平均。微涡流表面更新模型预测 kL‾=αoSc-1/2(νϵ‾)1/4$overline{{k}_{L}}={alpha }_{o}S{c}^{-1/2}{left(\nu\overline{\{epsilon}}}right)}^{1/4}$、其中,Sc$Sc$ 是分子施密特数,ν$\nu $ 是水的运动粘度,ϵ‾$overline{\{epsilon}}$ 是界面或界面附近的水侧平均湍流动能耗散率。虽然许多数据集都报告了 αo=0.39-0.46${\alpha }_{o}=0.39-0.46$,但其他数据集则报告了该值范围附近的巨大散差或变化。本文表明,这种分散可以部分地通过ϵ‾$overline{{epsilon}}$附近瞬时ϵ${epsilon}$的高时间变异性来解释,而这种机制是以前没有考虑过的。随着ϵ‾${epsilon}$的变异系数(CVe)$\left(C{V}_{e}\right)$的增加、αo${alpha }_{o}$ 必须通过乘数 (1+CVe2)-3/32${left(1+C{V}_{e}^{2}\right)}^{-3/32}$ 进行调整,该乘数是根据ϵ${epsilon}$ 的概率密度函数的对数正态模型得出的。据报道,αo${α }_{o}$随大尺度雷诺数的变化也可部分归因于ϵ$\{epsilon}$的间歇效应。这种间歇性的特征是ϵ${epsilon}$的长程(即幂律衰减)空间自相关函数。αo$\{alpha }_{o}$ 随大尺度雷诺数变化并不一定违反微涡流模型。相反,它表明了能量级联中能量跨尺度传递所产生的宏观与微观尺度之间的协调。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Gas Transfer Across Air-Water Interfaces in Inland Waters: From Micro-Eddies to Super-Statistics
In inland water covering lakes, reservoirs, and ponds, the gas exchange of slightly soluble gases such as carbon dioxide, dimethyl sulfide, methane, or oxygen across a clean and nearly flat air-water interface is routinely described using a water-side mean gas transfer velocity kL$\overline{{k}_{L}}$, where overline indicates time or ensemble averaging. The micro-eddy surface renewal model predicts kL=αoSc1/2(νϵ)1/4$\overline{{k}_{L}}={\alpha }_{o}S{c}^{-1/2}{\left(\nu \overline{{\epsilon}}\right)}^{1/4}$, where Sc$Sc$ is the molecular Schmidt number, ν$\nu $ is the water kinematic viscosity, and ϵ$\overline{{\epsilon}}$ is the waterside mean turbulent kinetic energy dissipation rate at or near the interface. While αo=0.390.46${\alpha }_{o}=0.39-0.46$ has been reported across a number of data sets, others report large scatter or variability around this value range. It is shown here that this scatter can be partly explained by high temporal variability in instantaneous ϵ${\epsilon}$ around ϵ$\overline{{\epsilon}}$, a mechanism that was not previously considered. As the coefficient of variation (CVe)$\left(C{V}_{e}\right)$ in ϵ${\epsilon}$ increases, αo${\alpha }_{o}$ must be adjusted by a multiplier (1+CVe2)3/32${\left(1+C{V}_{e}^{2}\right)}^{-3/32}$ that was derived from a log-normal model for the probability density function of ϵ${\epsilon}$. Reported variations in αo${\alpha }_{o}$ with a macro-scale Reynolds number can also be partly attributed to intermittency effects in ϵ${\epsilon}$. Such intermittency is characterized by the long-range (i.e., power-law decay) spatial auto-correlation function of ϵ${\epsilon}$. That αo${\alpha }_{o}$ varies with a macro-scale Reynolds number does not necessarily violate the micro-eddy model. Instead, it points to a coordination between the macro- and micro-scales arising from the transfer of energy across scales in the energy cascade.
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来源期刊
Water Resources Research
Water Resources Research 环境科学-湖沼学
CiteScore
8.80
自引率
13.00%
发文量
599
审稿时长
3.5 months
期刊介绍: Water Resources Research (WRR) is an interdisciplinary journal that focuses on hydrology and water resources. It publishes original research in the natural and social sciences of water. It emphasizes the role of water in the Earth system, including physical, chemical, biological, and ecological processes in water resources research and management, including social, policy, and public health implications. It encompasses observational, experimental, theoretical, analytical, numerical, and data-driven approaches that advance the science of water and its management. Submissions are evaluated for their novelty, accuracy, significance, and broader implications of the findings.
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