Stability analysis of asymmetric wakes

The shear layer thickness asymmetry effects on the incompressible inviscid asymmetric wakes are examined by means of both temporal and spatiotemporal stability analyses. To allow for the variation of the shear layer thicknesses on either side of the wake, a family of piecewise linear velocity profiles is introduced. The temporal stability analysis shows that the maximum growth rate of the sinuous mode is dominated by the shear layer thickness of the thinner side and the maximum growth rate of the varicose mode is dominated by the thicker side. The sinuous mode is more unstable than the varicose mode, and increasing the degree of asymmetry would increase the growth rate difference between the sinuous instability and the varicose instability. The spatiotemporal analysis shows that increasing the degree of asymmetry generally has a stabilizing effect. In particular, the influences of shear layer thickness on the absolute growth rate can be classified into three different regions: In region I, increasing shear layer thickness at either side would destabilize the flow. In region II, increasing the degree of symmetry has a destabilizing effect. In region III, decreasing shear layer thickness at either side would destabilize the flow. These findings provide us some information on how to control asymmetric wakes. Furthermore, we find that the frequency of the most absolutely unstable mode is mainly determined by the total shear layer thickness and has a slight dependence on the asymmetry ratio.