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On the starting process of strongly nonlinear vortex/Rayleigh-wave interactions

Part of: Incompressible viscous fluids

Published online by Cambridge University Press:  26 February 2010

P. G. Brown ,
S. N. Brown ,
F. T. Smith  and
S. N. Timoshin
P. G. Brown
Affiliation:
9 Esparto Street, London. SW18 4DQ.
S. N. Brown
Affiliation:
Department of Mathematics, University College London, Gower Street, London. WC1E6BT.
F. T. Smith
Affiliation:
Department of Mathematics, University College London, Gower Street, London. WC1E6BT.
S. N. Timoshin
Affiliation:
Department of Mathematics, University College London, Gower Street, London. WC1E6BT.
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Abstract

An oncoming two-dimensional laminar boundary layer that develops an unstable inflection point and becomes three-dimensional is described by the Hall-Smith (1991) vortex/wave interaction equations. These equations are now examined in the neighbourhood of the position where the critical surface starts to form. A consistent structure is established in which an inviscid core flow is matched to a viscous buffer-layer solution where the appropriate jump condition on the transverse shear stress is satisfied. The final result is a bifurcation equation for the (constant) amplitude of the wave pressure. A representative classical velocity profile is considered to illustrate solutions of this equation for a range of values of the wave-numbers.

MSC classification

Secondary: 76D10: Boundary-layer theory, separation and reattachment, higher-order effects
Type
Research Article
Information
Mathematika , Volume 40 , Issue 1 , June 1993 , pp. 7 - 29
Copyright
Copyright © University College London 1993

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