Vortex rigid motion in quasi-geostrophic shallow-water equations

TL;DR

This paper proves the existence of specific vortex configurations called V-states in quasi-geostrophic shallow-water equations, using bifurcation methods to identify multiple solutions with complex shapes.

Contribution

It introduces a bifurcation approach to establish the existence of doubly-connected V-states with holes for large m in quasi-geostrophic shallow-water equations.

Findings

Existence of relative equilibria with holes proven.

Two branches of m-fold doubly-connected V-states identified.

Bifurcation techniques applied to arbitrary-sized annuli.

Abstract

In this paper, we prove the existence of relative equilibria with holes for quasi-geostrophic shallow-water equations. More precisely, using bifurcation techniques, we establish for any m large enough the existence of two branches of m-fold doubly-connected V-states bifurcating from any annulus of arbitrary size.