Prandtl–Batchelor Flow in a Cylindrical Domain

IF 1.9 4区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Applied Mathematics Pub Date : 2024-07-31 DOI:10.1137/24m1637313

Emmanuel Dormy, H. Keith Moffatt

引用次数: 0

Abstract

SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1658-1667, August 2024.
Abstract. In this paper, the classical problem of two-dimensional flow in a cylindrical domain, driven by a nonuniform tangential velocity imposed at the boundary, is reconsidered in straightforward manner. When the boundary velocity is a pure rotation [math] plus a small perturbation [math] and when the Reynolds number based on [math] is large (Re [math]), this flow is of “Prandtl–Batchelor” type, namely, a flow of uniform vorticity [math] in a core region inside a viscous boundary layer of thickness O(Re)[math]. The O[math] contribution to [math] is determined here by asymptotic analysis up to O[math]. The result is in good agreement with numerical computation for Re [math].

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圆柱形域中的普朗特-巴歇尔流

SIAM 应用数学杂志》，第 84 卷第 4 期，第 1658-1667 页，2024 年 8 月。摘要本文以直截了当的方式重新考虑了在边界施加非均匀切向速度驱动下圆柱形域中二维流动的经典问题。当边界速度为纯旋转[math]加小扰动[math]，且基于[math]的雷诺数较大（Re[math]）时，这种流动属于 "普朗特-巴歇尔 "类型，即在厚度为 O(Re)[math] 的粘性边界层内的核心区域中存在均匀涡度[math]的流动。这里通过直到 O[math] 的渐近分析确定了 O[math] 对[math]的贡献。结果与 Re [math] 的数值计算结果非常吻合。

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 Applied Mathematics 数学-应用数学

CiteScore

3.60

自引率

0.00%

发文量

审稿时长

12 months

期刊介绍： SIAM Journal on Applied Mathematics (SIAP) is an interdisciplinary journal containing research articles that treat scientific problems using methods that are of mathematical interest. Appropriate subject areas include the physical, engineering, financial, and life sciences. Examples are problems in fluid mechanics, including reaction-diffusion problems, sedimentation, combustion, and transport theory; solid mechanics; elasticity; electromagnetic theory and optics; materials science; mathematical biology, including population dynamics, biomechanics, and physiology; linear and nonlinear wave propagation, including scattering theory and wave propagation in random media; inverse problems; nonlinear dynamics; and stochastic processes, including queueing theory. Mathematical techniques of interest include asymptotic methods, bifurcation theory, dynamical systems theory, complex network theory, computational methods, and probabilistic and statistical methods.