Instability of strained counter-rotating vortices

Abstract

The stability of counter-rotating vortices subjected to a uniform plane straining flow has been examined in this study. The straining flow field flattens the vortices in a way that the resulting slender shape can be considered as a double shear layer. The linear analysis based on this assumption has indicated two regions of instability: decreasing slenderness ratio and increasing slenderness ratio with time, where the Orr–Sommerfeld equation has been found to describe the phenomenon when the slenderness ratio is time independent. Decreasing slenderness ratio with time, coupled with an extension of the line vortex, is a stabilizing mechanism, where the rate of change of the slenderness ratio plays an important role in this process. On the other hand, in the case of a contracting line vortex with decreasing slenderness ratio, instability will not reach full growth and the vortex will undergo irreversible elongation. Increasing slenderness ratio is found to be an unconditionally destabilizing mechanism. The nonlinear phenomenon, computed by the numerical solution, indicates that in the case of an extending line vortex and decreasing slenderness ratio, the vortices will collapse to form a pair of vortices with finite cores. In some other cases, the vortex pair will undergo irreversible elongation, where increased slenderness ratio is found numerically to be a destabilizing mechanism.