论湍流的几何

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics Pub Date : 2025-09-11 DOI:10.1016/j.geomphys.2025.105646

Valentin Lychagin

{"title":"论湍流的几何","authors":"Valentin Lychagin","doi":"10.1016/j.geomphys.2025.105646","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we apply the method of geometrization of random vectors <span><span>[1]</span></span> to turbulent media, which we understand as random vector fields on base manifolds. This gives rise to various geometric structures on the tangent as well as cotangent bundles. Among these, the most important is the Mahalanobis metric on the tangent bundle, which allows us to obtain all the necessary ingredients for implementing the scheme <span><span>[2]</span></span> to the description of flows in turbulent media. As an illustration, we consider the applications to flows of real gases based on Maxwell–Boltzmann statistics.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"217 ","pages":"Article 105646"},"PeriodicalIF":1.2000,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On geometry of turbulent flows\",\"authors\":\"Valentin Lychagin\",\"doi\":\"10.1016/j.geomphys.2025.105646\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>In this paper, we apply the method of geometrization of random vectors <span><span>[1]</span></span> to turbulent media, which we understand as random vector fields on base manifolds. This gives rise to various geometric structures on the tangent as well as cotangent bundles. Among these, the most important is the Mahalanobis metric on the tangent bundle, which allows us to obtain all the necessary ingredients for implementing the scheme <span><span>[2]</span></span> to the description of flows in turbulent media. As an illustration, we consider the applications to flows of real gases based on Maxwell–Boltzmann statistics.</div></div>\",\"PeriodicalId\":55602,\"journal\":{\"name\":\"Journal of Geometry and Physics\",\"volume\":\"217 \",\"pages\":\"Article 105646\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2025-09-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Geometry and Physics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0393044025002311\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Geometry and Physics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0393044025002311","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

本文将随机向量[1]的几何化方法应用于湍流介质，我们将其理解为基流形上的随机向量场。这就产生了切线和共切线束上的各种几何结构。其中，最重要的是切线束上的马氏度规，它使我们能够获得实现方案[2]来描述湍流介质中流动的所有必要成分。作为一个例子，我们考虑了基于麦克斯韦-玻尔兹曼统计在实际气体流动中的应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

On geometry of turbulent flows

In this paper, we apply the method of geometrization of random vectors [1] to turbulent media, which we understand as random vector fields on base manifolds. This gives rise to various geometric structures on the tangent as well as cotangent bundles. Among these, the most important is the Mahalanobis metric on the tangent bundle, which allows us to obtain all the necessary ingredients for implementing the scheme [2] to the description of flows in turbulent media. As an illustration, we consider the applications to flows of real gases based on Maxwell–Boltzmann statistics.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Journal of Geometry and Physics 物理-物理：数学物理

CiteScore

2.90

自引率

6.70%

发文量

205

审稿时长

64 days

期刊介绍： The Journal of Geometry and Physics is an International Journal in Mathematical Physics. The Journal stimulates the interaction between geometry and physics by publishing primary research, feature and review articles which are of common interest to practitioners in both fields. The Journal of Geometry and Physics now also accepts Letters, allowing for rapid dissemination of outstanding results in the field of geometry and physics. Letters should not exceed a maximum of five printed journal pages (or contain a maximum of 5000 words) and should contain novel, cutting edge results that are of broad interest to the mathematical physics community. Only Letters which are expected to make a significant addition to the literature in the field will be considered. The Journal covers the following areas of research: Methods of: • Algebraic and Differential Topology • Algebraic Geometry • Real and Complex Differential Geometry • Riemannian Manifolds • Symplectic Geometry • Global Analysis, Analysis on Manifolds • Geometric Theory of Differential Equations • Geometric Control Theory • Lie Groups and Lie Algebras • Supermanifolds and Supergroups • Discrete Geometry • Spinors and Twistors Applications to: • Strings and Superstrings • Noncommutative Topology and Geometry • Quantum Groups • Geometric Methods in Statistics and Probability • Geometry Approaches to Thermodynamics • Classical and Quantum Dynamical Systems • Classical and Quantum Integrable Systems • Classical and Quantum Mechanics • Classical and Quantum Field Theory • General Relativity • Quantum Information • Quantum Gravity