Transport of vorticity through a finite channel

Abstract

The paper addresses the plane inviscid incompressible flows through a finite duct. The boundary conditions are: the normal velocity is given at both inlet and outlet cross-sections, and in addition vorticity is given at the inlet. Attention is focused on effects of these boundary conditions on dynamics of vorticity. We study evolution of perturbations of steady flows and show that at there are least three qualitatively different possibilities: first, the perturbations can be washed out the duct completely in a finite time; second, they can be trapped in the duct and then form some steady vortex structures; third, they can develop themselves into an unsteady pulsating flow.