An analytical and numerical study of steady patches in the disc

2015/10/06 by de la Hoz, Francisco, Hassainia, Zineb, Hmidi, Taoufik +1 · 3 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1510.01550

Abstract

In this paper, we prove the existence of m-fold rotating patches for the Euler equations in the disc, for both simply-connected and doubly-connected cases. Compared to the planar case, the rigid boundary introduces rich dynamics for the lowest symmetries m=1 and m=2. We also discuss some numerical experiments highlighting the interaction between the boundary of the patch and the rigid one.

Cited by

• Desingularization of nondegenerate rotating vortex patches
• Steady vortex-patch flows with circulation past an obstacle in an infinity long strip
• Large-amplitude periodic solutions to the steady Euler equations with piecewise constant vorticity

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