K\'arm\'an Vortex Street in incompressible fluid models

Abstract

This paper aims to provide a robust model for the well-known phenomenon of K\'arm\'an Vortex Street arising in Fluid Mechanics. The first theoretical attempt to model this pattern was given by von K\'arm\'an [22, 23]. He considered two parallel staggered rows of point vortices, with opposite strength, that translate at the same speed. Following the ideas of Saffman and Schatzman [36], we propose to study this phenomenon in the Euler equations by considering two infinite arrows of vortex patches. The key idea is to desingularize the point vortex model proposed by von K\'arm\'an. Our construction is flexible and can be extended to more general incompressible models.