Gas Transfer Across Air-Water Interfaces in Inland Waters: From Micro-Eddies to Super-Statistics

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":"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\" 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":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Water Resources Research","FirstCategoryId":"89","ListUrlMain":"https://doi.org/10.1029/2023wr036615","RegionNum":1,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENVIRONMENTAL SCIENCES","Score":null,"Total":0}
引用次数: 0

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 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.
内陆水域气-水界面的气体传输:从微电子到超统计
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。
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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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