Waves Generated by Shear Layer Instabilities

Abstract

Stern & Adam and subsequent workers have considered the linear stability of two-dimensional, parallel, ideal fluid flow with shear in the presence of a free surface. In these studies a fluid current is modelled as a finite layer of constant vorticity above a semi-infinite stagnant region, corresponding to a piecewise-linear velocity profile. Here, an investigation of the stability of currents for several smooth velocity profiles is presented. With surface tension present it is found that the fluid surface velocity must still exceed the minimum wavespeed of stagnant fluid for instability to occur; a result highlighted by Caponi et al. for piecewise-linear profiles. Instability growth rates are found to be significantly smaller than those associated with a piecewise-linear profile. There are also qualitative differences in the stability characteristics; in particular, transition is associated with an exchange of stability for smooth profiles, but not for the piecewise-linear profile.