Absolute stability of a Bénard-von Kármán vortex street in a confined geometry

Matière et Systèmes Complexes, CNRS and Université Paris Diderot UMR 7057 - Bâtiment Condorcet, 10 rue Alice Domon et Léonie Duquet, 75013 Paris, France

Received: 21 October 2016
Accepted: 14 February 2017

Abstract

We have investigated the stability of a double vortex street, induced in a rectangular container by a tape, or a rope, moving at high speed on its free surface. Depending on the tape velocity and on the geometrical aspect ratios, three patterns of flows are observed: 1) a vortex street with recirculation of the liquid along the lateral sides of the container, 2) the same recirculation but with no stable vortex array, 3) recirculation along the bottom of the container. We have investigated the spatial structure of the vortex street and found that this system explores the phase space available inside a stability tongue predicted at the end of the 1920s by Rosenhead for point vortices in a perfect fluid. Although this very surprising result contrasts with the well-known von Kármán unique stability condition for point vortex streets in an infinite domain, this complements the theory inside a channel of finite breadth. In this paper, we present the very first experimental confirmation of this 90-year-old theory.