Stability analysis of regularized viscous vortex sheets
Bull. Korean Math. Soc. 2016 Vol. 53, No. 3, 843-852
Published online May 31, 2016
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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