切变流线性不稳定性的简单证明及其在涡片上的应用

IF 1.3 3区数学 Q2 MATHEMATICS, APPLIED

Journal of Mathematical Fluid Mechanics Pub Date : 2025-05-05 DOI:10.1007/s00021-025-00937-z

Anuj Kumar, Wojciech Ożański

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引用次数: 0

摘要

本文考虑Lin （SIAM J .数学学报，35(2):318-356,2003）提出的平行剪切流线性失稳的构造。我们给出了该问题在Sobolev设置下的另一种简单证明，揭示了Plemelj-Sochocki公式在不稳定性出现时的数学作用，并且不需要锥条件。此外，我们还对该方法进行了局部化，得到了平面涡旋片的开尔文-亥姆霍兹不稳定性的近似。

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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A Simple Proof of Linear Instability of Shear Flows with Application to Vortex Sheets

We consider the construction of linear instability of parallel shear flows, which was developed by Lin (SIAM J Math Anal 35(2):318–356, 2003). We give an alternative simple proof in Sobolev setting of the problem, which exposes the mathematical role of the Plemelj–Sochocki formula in the emergence of the instability, as well as does not require the cone condition. Moreover, we localize this approach to obtain an approximation of the Kelvin–Helmholtz instability of a flat vortex sheet.

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来源期刊

Journal of Mathematical Fluid Mechanics 物理-力学

CiteScore

2.00

自引率

15.40%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Mathematical Fluid Mechanics (JMFM)is a forum for the publication of high-quality peer-reviewed papers on the mathematical theory of fluid mechanics, with special regards to the Navier-Stokes equations. As an important part of that, the journal encourages papers dealing with mathematical aspects of computational theory, as well as with applications in science and engineering. The journal also publishes in related areas of mathematics that have a direct bearing on the mathematical theory of fluid mechanics. All papers will be characterized by originality and mathematical rigor. For a paper to be accepted, it is not enough that it contains original results. In fact, results should be highly relevant to the mathematical theory of fluid mechanics, and meet a wide readership.