On the stability of vortex streets in a stratified fluid

Abstract

On the basis of the perturbation theory developed previously by the authors for localized hydrodynamic vortices, the influence of a specified jet flow and of the structure of individual vortices on the stability of the Karman street is investigated. It is shown that, for a street of vortices with a power law of decrease in the azimuthal velocity, the jet flow suppresses instability only with respect to perturbations with wavelengths from a certain range determined by the parameters of the flow. At the same time, for streets formed from vortices with a Gaussian profile of the azimuthal velocity, even in the absence of a specified flow, there is a certain region of the street’s parameters in which the street is stable against perturbations of all scales. Thus, for the purposes of modeling quasi-two-dimensional flows in a stratified fluid by a sequence of localized vortices, which is discussed in this study, vortices with a Gaussian profile of the azimuthal velocity turn out to be preferable. The results of this study are consistent with numerous experiments on the structure of a quasi-two-dimensional wake behind a body in a stratified fluid at large Reynolds and Froude numbers.