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

TL;DR

This paper introduces a computational method to resolve degeneracies in infinite channel shear flows by applying symmetry-breaking perturbations, revealing new nonlinear solutions without classical stability analysis.

Contribution

It presents a simple computational approach to break flow symmetries and uncover higher order nonlinear solutions in shear layers with perturbations.

Findings

Resolved degeneracy in shear flow bifurcations

Discovered new nonlinear solutions in perturbed flows

Demonstrated effectiveness without classical stability theory

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.