Geodesic
Instability to longitudinal vortices in wavy shear flow
W. R.C. Phillips1 ; Q. Shen1 ; Z. Wu1
1Department of Theoretical and Applied Mechanics University of Illinois at Urbana-Champaign Urbana IL 61801-2935, USA
ESAIM. Proceedings, Tome 1 (1996), pp. 295-305
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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.
DOI : 10.1051/proc:1996025

W. R.C. Phillips  1   ; Q. Shen  1   ; Z. Wu  1

1 Department of Theoretical and Applied Mechanics University of Illinois at Urbana-Champaign Urbana IL 61801-2935, USA 
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W. R.C. Phillips; Q. Shen; Z. Wu. Instability to longitudinal vortices in wavy shear flow. ESAIM. Proceedings, Tome 1 (1996), pp. 295-305. doi: 10.1051/proc:1996025

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