Instability to longitudinal vortices in wavy shear flow
Department of Theoretical and Applied Mechanics University of Illinois at Urbana-Champaign Urbana IL 61801-2935, USA
Initially spanwise-independent small but finite-amplitude two-dimensional rotational waves and their nonlinear interaction with unidirectional O(1) shear flows are reviewed from the viewpoint of their instability to longitudinal vortex form. The wave-mean interaction is described by a generalized Lagrangian-mean formulation in combination with a separate theory to account for the back effect of the developing mean flow on the wave field. Both the inviscid and viscid eigenvalue problems relevant to the instability are discussed.
© EDP Sciences, ESAIM, 1996