Linear instability of a corrugated vortex sheet

Abstract

The linear inviscid instability of an infinitely thin vortex sheet, periodically corrugated with finite amplitude along the spanwise direction, is investigated analytically. Two types of corrugations are studied, one of which includes the presence of an impermeable wall. Exact eigensolutions are found in the limit of a very long wavelength. The sheets are unstable to both sinuous and varicose disturbances. The former is generally found to be more unstable, although the difference only appears for finite wavelengths. The effect of the corrugation is shown to be stabilizing, although in the wall-bounded sheet the effect is partly compensated by the increase in the distance from the wall. The instability is traced to a pair of oblique Kelvin-Helmholtz waves in the flat-sheet limit.