On the Boussinesq Hypothesis for a Stochastic Proudman–Taylor Model

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Mathematical Analysis Pub Date : 2024-06-03 DOI:10.1137/23m1587944

Franco Flandoli, Dejun Luo

引用次数: 0

Abstract

SIAM Journal on Mathematical Analysis, Volume 56, Issue 3, Page 3886-3923, June 2024.
Abstract. We introduce a stochastic version of the Proudman–Taylor model, a 2D-3C fluid approximation of the 3D Navier–Stokes equations, with the small-scale turbulence modeled by a transport-stretching noise. For this model we may rigorously take a scaling limit leading to a deterministic model with additional viscosity on large scales. In certain choice of noises without mirror symmetry, we identify an anisotropic kinetic alpha (AKA) effect. This is the first example with a 3D structure and a stretching noise term.

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论随机普鲁德曼-泰勒模型的布辛斯克假说

SIAM 数学分析期刊》，第 56 卷，第 3 期，第 3886-3923 页，2024 年 6 月。摘要。我们介绍了 Proudman-Taylor 模型的随机版本，它是三维纳维-斯托克斯方程的二维-三维流体近似，小尺度湍流由传输拉伸噪声建模。对于这个模型，我们可以通过严格的缩放极限，得到一个在大尺度上具有额外粘性的确定性模型。在某些没有镜像对称性的噪声选择中，我们发现了各向异性动力学阿尔法（AKA）效应。这是第一个具有三维结构和拉伸噪声项的例子。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

SIAM Journal on Mathematical Analysis 数学-应用数学

CiteScore

3.30

自引率

5.00%

发文量

175

审稿时长

12 months

期刊介绍： SIAM Journal on Mathematical Analysis (SIMA) features research articles of the highest quality employing innovative analytical techniques to treat problems in the natural sciences. Every paper has content that is primarily analytical and that employs mathematical methods in such areas as partial differential equations, the calculus of variations, functional analysis, approximation theory, harmonic or wavelet analysis, or dynamical systems. Additionally, every paper relates to a model for natural phenomena in such areas as fluid mechanics, materials science, quantum mechanics, biology, mathematical physics, or to the computational analysis of such phenomena. Submission of a manuscript to a SIAM journal is representation by the author that the manuscript has not been published or submitted simultaneously for publication elsewhere. Typical papers for SIMA do not exceed 35 journal pages. Substantial deviations from this page limit require that the referees, editor, and editor-in-chief be convinced that the increased length is both required by the subject matter and justified by the quality of the paper.