On the etiology of shear layer vortices

In an effort to isolate the mechanism by which streamwise structures form in turbulent wall layers, evolution equations were derived for the streamwise velocity and vorticity perturbations about a mean turbulent fully developed channel flow. The stability of these equations, which take their most concise form when derived from the Generalized Lagrangian mean equations of Andrews and McIntyre, are studied assuming normal modes and infinitesimal disturbances. The resulting stability diagram yields, inter alia, the spanwise periodicity of the resulting structures, which we term shear layer vortices. If streaks are thought of as the footprints of these vortices, we then have a formal way of determining the spacing of streaks. The first three modes of instability are determined; at the first not just two vortices form per period, but four. It is also evident that an intense local shear layer forms about the plane in which the convection velocity equals the mean Eulerian velocity.Dedicated to Professor J.L. Lumley on the occasion of his 60th birthday.This work was supported in part by the U.S. Office of Naval Research under SRO IV Grant No. N00014-85-K-0172 and in part by the National Science Foundation Grant CTS-9008477.