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arXiv · 2010.08194

Co-rotating vortices with N fold symmetry for the inviscid surface quasi-geostrophic equation

Ludovic Godard-Cadillac·Philippe Gravejat·Didier Smets
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Abstract

We provide a variational construction of special solutions to the generalized surface quasi-geostrophic equations. These solutions take the form of N vortex patches with N-fold symmetry , which are steady in a uniformly rotating frame. Moreover, we investigate their asymptotic properties when the size of the corresponding patches vanishes. In this limit, we prove these solutions to be a desingularization of N Dirac masses with the same intensity, located on the N vertices of a regular polygon rotating at a constant angular velocity.

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Ludovic Godard-Cadillac, Philippe Gravejat, Didier Smets. 2020-10-16. Co-rotating vortices with N fold symmetry for the inviscid surface quasi-geostrophic equation. https://arxiv.org/abs/2010.08194

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