Onset of mixing layer instability in flow past a plate

Abstract

A global stability analysis of the flow past a flat plate, normal to the flow, is carried out to determine the critical Re for the onset of convective instability of the mixing-layer-type modes. To suppress the primary wake mode, which leads to von Karman vortex shedding, flow past one half of the plate is studied and symmetry conditions are enforced along the wake centerline. The linearized perturbation equations for an incompressible flow are written in a moving frame of reference that travels with the perturbation and solved using a stabilized finite element method. The critical Re for the onset of convective instability is found to be 22, approximately, for H=5. Here, H is the distance of the lateral boundary from the plate centerline. Computations have also been carried out for H=10 and 20. The critical Re decreases with increase in H. Excellent agreement is observed between the results from global stability analysis and direct time integration of linearized disturbance equations. The results from the global analysis are compared with earlier reported results from local analysis of a Gaussian wake profile.