Hopf bifurcation of a non-parallel Navier-Stokes flow

Abstract

A plane non-parallel flow in a square fluid domain exhibits an odd number of vortices. A spectral structure is found to have a non-real solution of the spectral problem linearized around the flow. With the use of this structure, Hopf bifurcation or secondary time periodic flows branching of a basic square eddy flow is found. In contrast to a square eddy flow involving an even number of vortices in earlier analytical and experimental investigations, instability of the flow leads to steady-state bifurcations.