Prandtl-Batchelor flows on an annulus

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-10-30 DOI:10.1016/j.aim.2024.109994

Mingwen Fei , Chen Gao , Zhiwu Lin , Tao Tao

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引用次数: 0

Abstract

For steady two-dimensional Navier-Stokes flows with a single eddy (i.e. nested closed streamlines) in a simply connected domain, Prandtl (1905) and Batchelor (1956) found that in the inviscid limit, the vorticity is constant inside the eddy. In this paper, we consider the generalized Prandtl-Batchelor theory for the forced steady Navier-Stokes equations on an annulus. First, we observe that in the limit of infinite Reynolds number, if the streamlines of forced steady Navier-Stokes solutions on an annulus are nested closed, then the inviscid limit is a rotating shear flow uniquely determined by the external force and boundary conditions. We call solutions of steady Navier-Stokes equations with the above property Prandtl-Batchelor flows. Then, by constructing higher order approximate solutions of the forced steady Navier-Stokes equations and establishing the validity of Prandtl boundary layer expansion, we give a rigorous proof of the existence of Prandtl-Batchelor flows on an annulus with the wall velocities slightly different from the rigid-rotations along the same direction.

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环面上的普氏流

对于简单连接域中具有单一涡流（即嵌套封闭流线）的稳定二维纳维-斯托克斯流，Prandtl（1905 年）和 Batchelor（1956 年）发现，在不粘性极限中，涡流内部的涡度是恒定的。在本文中，我们考虑了环面上受迫稳定纳维-斯托克斯方程的广义普朗特-巴彻勒理论。首先，我们观察到，在无限雷诺数极限下，如果环面上的强制稳定 Navier-Stokes 解的流线是嵌套封闭的，那么不粘性极限就是由外力和边界条件唯一决定的旋转剪切流。我们将具有上述性质的稳定纳维-斯托克斯方程的解称为普朗特-巴切洛流。然后，通过构建受迫稳定纳维-斯托克斯方程的高阶近似解，并建立普朗特边界层扩展的有效性，我们给出了在环面上存在普朗特-巴歇尔流的严谨证明，其壁面速度与沿同一方向的刚体旋转速度略有不同。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.