Bulletin of the
Korean Mathematical Society
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ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2016; 53(3): 843-852

Printed May 31, 2016

https://doi.org/10.4134/BKMS.b150380

Copyright © The Korean Mathematical Society.

Stability analysis of regularized viscous vortex sheets

Sung-Ik Sohn

Gangneung-Wonju National University

Abstract

A vortex sheet is susceptible to the Kelvin-Helmhotz instability, which leads to a singularity at finite time. The vortex blob model provided a regularization for the motion of vortex sheets in an inviscid fluid. In this paper, we consider the blob model for viscous vortex sheets and present a linear stability analysis for regularized sheets. We show that the diffusing viscous vortex sheet is unstable to small perturbations, regardless of the regularization, but the viscous sheet in the sharp limit becomes stable, when the regularization is applied. Both the regularization parameter and viscosity damp the growth rate of the sharp viscous vortex sheet for large wavenumbers, but the regularization parameter gives more significant effects than viscosity.

Keywords: vortex sheet, viscous diffusion, blob-regularization, linear stability

MSC numbers: Primary 76E05, 76E17, 76D17

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