On the linear stability of the inviscid Kármán vortex street

Abstract

The classical point-vortex model for a Kármán vortex street is linearly stable only for an isolated case. This property has been shown numerically to hold for other, more complicated, models of the same flow. It is shown here that it is a consequence of the Hamiltonian structure of the model, related to the codimension of the set of matrices with a particular Jordan block structure in the space of Hamiltonian matrices, and that it can be expected to hold generically for any two-dimensional inviscid array of vortices that has back-to-fore symmetry, and that is ‘close enough’ to the point-vortex model.