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• W2334264958 abstract "Chorin's vortex blob method has been proposed as a way to extend vortex sheet motion past the singularity formation time, into the physically important roll-up regime. Basic questions are: 1. Does the vortex blob method converge to an infinite spiral as the smoothing parameter tends to zero? 2. Do vortex blob computations approximate real fluid motion? This paper will present and discuss three computations which are relevant to these issues: a) periodic roll-up, b) wake patterns in a thin soap film, c) separation at a sharp edge. 1. Introduction. Coherent vortex structures occur in many types of fluid flow such as wakes, jets, and boundary layers. To make progress in the analysis of these flows, one may consider simpler models in which various physical effects are assumed to be small. In the vortex sheet model, a thin shear layer is replaced by a surface across which the tangential component of the fluid velocity has a jump discontinuity. The mathematical study of vortex sheets has advanced in recent years, but many important questions are still open. Vortex sheet motion belongs to the larger field of vortex dynamics, one of the main approaches to understanding fluid turbulence. Careful numerical experiments have played a key role in advancing the analysis and application of the vortex sheet model. Difficulties arise in computing vortex sheet motion due to short wavelength instability, singu­ larity formation, and spiral roll-up. Chorin's vortex blob method (10,11), in which the vortex sheet's velocity is desingularized, has been proposed to deal with these difficulties. Basic questions concerning this approach are: 1. Does the vortex blob method converge to an infinite spiral as the smoothing parameter tends to zero?" @default.
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• W2334264958 date "1991-01-01" @default.
• W2334264958 modified "2023-09-26" @default.
• W2334264958 title "Vortex Sheet Computations: Roll-Up, Wakes, Separation" @default.
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