Subcritical bifurcations of shear flows

Abstract

It is well-known that shear flows in a strip or in the half plane are unstable for the incompressible Navier-Stokes equations if the viscosity $\hat{I}½$ is small enough, provided the horizontal wave number $\hat{I}\pm$ lies in a small interval, between the so called lower and upper marginal stability curves. Moreover, a Hopf bifurcation occurs at the upper marginal stability curve. In this article, for various shear flows, we give numerical evidences that this bifurcation is subcritical.