On concentrated traveling vortex pairs with prescribed impulse

TL;DR

This paper investigates the existence, stability, and asymptotic behavior of concentrated traveling vortex pairs with prescribed impulse, providing new insights into vortex dynamics and stability analysis.

Contribution

It introduces a constrained maximization framework for vortex pairs, proving existence and stability, and derives asymptotic estimates for large impulse vortex pairs.

Findings

Existence of stable traveling vortex pairs with prescribed impulse

Asymptotic approach to point vortex pairs with opposite signs

Stability results for Chaplygin-Lamb dipole in non-concentrated case

Abstract

In this paper, we consider a constrained maximization problem related to planar vortex pairs with prescribed impulse. We prove existence, stability and asymptotic behavior for the maximizers, hence obtain a family of stable traveling vortex pairs approaching a pair of point vortices with equal magnitude and opposite signs. As a corollary, we get fine asymptotic estimates for Burton's vortex pairs with large impulse. For the non-concentrated case, we prove a form of stability for the Chaplygin-Lamb dipole.