Free access article

ESAIM: Proc., 1996, Vol. 1, pp. 295-305
DOI: 10.1051/proc:1996025

Instability to longitudinal vortices in wavy shear flow

W.R.C. Phillips, Q. Shen and Z. Wu

Department of Theoretical and Applied Mechanics University of Illinois at Urbana-Champaign Urbana IL 61801-2935, USA

Abstract
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

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