Onset of shear layer instability in flow past a cylinder

Abstract

Global stability analysis of the flow past a cylinder is carried out to determine the critical Re for the onset of shear layer instability. To suppress the wake mode that leads to von Kármán vortex shedding, flow past one-half of the cylinder is studied. 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 approximately 54. Excellent agreement is observed between the results from global stability analysis and direct time integration of linearized disturbance equations. The wake and shear layer modes for a full cylinder are compared. Results are also presented for stability analysis of the time-averaged flow.