{"title":"A Gauge-Invariant Lagrangian Determined by the n-Point Probability Density Function of a Vorticity Field of Wave Optical Turbulence","authors":"V. N. Grebenev, A. N. Grishkov","doi":"10.1134/s1028335823120042","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The geometric methods for Yang–Mills fields of gauge transformations are applied to find an invariant Lagrangian in the fiber bundle of the configuration of 2<i>d</i> space <i>X</i> of a turbulent flow determined by the <i>n</i>-point probability density function (PDF) <i>f</i><sub><i>n</i></sub>. The two-dimensional wave optical turbulence is considered in the case of an inverse cascade of turbulence energy transfer under external impacts in the form of white Gaussian noise and large-scale friction. The <i>n</i>-point PDF of the vorticity field satisfies the <i>f</i><sub><i>n</i></sub>-equation from the Lundgren–Monin–Novikov hierarchy, and the conditions of equation invariance under external action are found. A Lagrangian, which is invariant relative to the <span>\\(H \\subset G\\)</span> subgroup (a group of the gauge transformations in the fiber bundle of the space <i>X</i>), and the conserved currents are constructed.</p>","PeriodicalId":533,"journal":{"name":"Doklady Physics","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Doklady Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1134/s1028335823120042","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MECHANICS","Score":null,"Total":0}
引用次数: 0
Abstract
The geometric methods for Yang–Mills fields of gauge transformations are applied to find an invariant Lagrangian in the fiber bundle of the configuration of 2d space X of a turbulent flow determined by the n-point probability density function (PDF) fn. The two-dimensional wave optical turbulence is considered in the case of an inverse cascade of turbulence energy transfer under external impacts in the form of white Gaussian noise and large-scale friction. The n-point PDF of the vorticity field satisfies the fn-equation from the Lundgren–Monin–Novikov hierarchy, and the conditions of equation invariance under external action are found. A Lagrangian, which is invariant relative to the \(H \subset G\) subgroup (a group of the gauge transformations in the fiber bundle of the space X), and the conserved currents are constructed.
摘要 应用杨-米尔斯场的规整变换几何方法，在由n点概率密度函数（PDF）fn决定的湍流的二维空间X构型的纤维束中寻找不变拉格朗日。在白高斯噪声和大尺度摩擦形式的外部冲击下，二维波光学湍流被视为湍流能量传递的反级联情况。涡度场的 n 点 PDF 满足 Lundgren-Monin-Novikov 层次中的 fn-方程，并找到了外部作用下方程不变性的条件。构建了相对于 \(H \subset G\) 子群（空间 X 纤维束中的轨距变换群）不变的拉格朗日和守恒电流。
期刊介绍：
Doklady Physics is a journal that publishes new research in physics of great significance. Initially the journal was a forum of the Russian Academy of Science and published only best contributions from Russia in the form of short articles. Now the journal welcomes submissions from any country in the English or Russian language. Every manuscript must be recommended by Russian or foreign members of the Russian Academy of Sciences.
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