Stability of Viscous Three-Dimensional Stratified Couette Flow via Dispersion and Mixing

IF 3.5 1区数学 Q1 MATHEMATICS

Communications on Pure and Applied Mathematics Pub Date : 2026-10-07 Epub Date: 2026-04-24 DOI:10.1002/cpa.70048

Michele Coti Zelati, Augusto Del Zotto, Klaus Widmayer

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引用次数: 0

Abstract

This article explores the stability of stratified Couette flow in the viscous $3 d$ Boussinesq equations. In this system, mixing effects arise from the shearing background, and gravity acts as a restoring force leading to dispersive internal gravity waves. These mechanisms are of fundamentally different nature and relevant in complementary dynamical regimes. Our study combines them to establish a bound for the non-linear transition threshold, which is quantitatively larger than the inverse Reynolds number $ν$ , and increases with stronger stratification resp. gravity.

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粘性三维分层库埃特流的分散和混合稳定性

本文探讨了粘性Boussinesq方程中分层Couette流的稳定性。在该系统中，剪切背景产生混合效应，重力作为恢复力导致内部重力波色散。这些机制具有根本不同的性质，并在互补的动力机制中相关。我们的研究将它们结合起来，建立了一个非线性过渡阈值的界限，该界限在定量上大于逆雷诺数，并且随着分层反应的增强而增加。重力。

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

Communications on Pure and Applied Mathematics 数学-数学

CiteScore

6.70

自引率

3.30%

发文量

审稿时长

>12 weeks

期刊介绍： Communications on Pure and Applied Mathematics (ISSN 0010-3640) is published monthly, one volume per year, by John Wiley & Sons, Inc. © 2019. The journal primarily publishes papers originating at or solicited by the Courant Institute of Mathematical Sciences. It features recent developments in applied mathematics, mathematical physics, and mathematical analysis. The topics include partial differential equations, computer science, and applied mathematics. CPAM is devoted to mathematical contributions to the sciences; both theoretical and applied papers, of original or expository type, are included.