Symmetry breaking perturbative flows to retrieve resonant modes in plane shear layers

Abstract

We propose a simple computational procedure in order to resolve the degeneracy, which invariably exists on the background of fluid motion associated with a channel of infinite extent. The procedure is applied to elucidate the bifurcation structure for the particular case of laterally heated flow with the addition of a perturbative Poiseuille flow component. The introduction of a symmetry breaking perturbation as the simplest imperfection alters the bifurcation tree of the original shear flow. As a result, the previously unknown higher order nonlinear solutions for the unperturbed flow are discovered, without implementing classical stability theory.