Traveling vortex pairs for 2D Boussinesq equations

TL;DR

This paper investigates the existence, behavior, and structure of traveling vortex pairs in 2D Boussinesq equations, providing new constructions and asymptotic analysis of vortex configurations.

Contribution

It introduces a novel family of traveling vortex pairs as a desingularization of point vortices and analyzes their asymptotic properties using an improved vorticity method.

Findings

Constructed a family of traveling vortex pairs.

Determined the limiting positions of vorticity supports.

Provided asymptotic descriptions of vortex configurations.

Abstract

In this paper, we study the existence and asymptotic properties of the traveling vortex pairs for the two-dimensional inviscid incompressible Boussinesq equations. We construct a family of traveling vorticity pairs, which constitutes the de-singularization of a pair of point vortices with equal intensity but opposite sign. Using the improved vorticity method, we also give limiting position of the supports of vorticities.