Kármán vortex street in incompressible fluid models
Claudia García
Abstract
Abstract This paper aims to provide a robust model for the well-known phenomenon of Kármán vortex street arising in fluid mechanics. The first theoretical attempt to model this pattern was given by von Kármán (1991 Göttinger Nachr., Math. Phys. Kl . 509–17); von Kármán (1912 Göttinger Nachr., Math. Phys. Kl . 547–56). 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 (1981 SIAM J. Sci. Stat. Comput . 2 285–95), 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 Kármán. Our construction is flexible and can be extended to more general incompressible models.