Hopf bifurcation of a non-parallel Navier-Stokes flow (Q6558307)

In this paper, the author study the existence of time periodic flows bifurcating from the non-parallel square eddy flow in the square domain \((0,N\pi)\times(0,N\pi)\) for an odd integer \(N\). He find a spectral structure which has a non-real solution of the spectral problem linearized around the flow. By making use of this structure, he find that Hopf bifurcation or secondary time periodic flows branching of a basic square eddy flow. In contrast to a square eddy flow involving an even number of vortices inearlier analytical and experimental investigations, instability of the flow leads to steady-state bifurcations.