Stability of vorticity defects in viscous shear

Abstract

The stability of viscous shear is studied for flows that consist of predominantly linear shear, but contain localized regions over which the vorticity varies rapidly. Matched asymptotic expansion simplifies the governing equations for the dynamics of such ‘vorticity defects’. The normal modes satisfy explicit dispersion relations. Nyquist methods are used to find and classify the possible instabilities. The defect equations are analysed in the inviscid limit to establish the connection with inviscid theory. Finally, the defect approximation is used to study nonlinear stability using weakly nonlinear techniques, and the initial value problem using Laplace transforms.