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Finite-amplitude effects on steady lee-wave patterns in subcritical stratified flow over topography

Published online by Cambridge University Press:  26 April 2006

T.-S. Yang  and
T. R. Akylas
T.-S. Yang
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
T. R. Akylas
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
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Abstract

The flow of a continuously stratified fluid over a smooth bottom bump in a channel of finite depth is considered. In the weakly nonlinear-weakly dispersive régime ε = a/h [Lt ] 1, μ = h/l [Lt ] 1 (where h is the channel depth and a, l are the peak amplitude and the width of the obstacle respectively), the parameter A = ε/μp (where p < 0 depends on the obstacle shape) controls the effect of nonlinearity on the steady lee wavetrain that forms downstream of the obstacle for subcritical flow speeds. For A = O(1), when nonlinear and dispersive effects are equally important, the interaction of the long-wave disturbance over the obstacle with the lee wave is fully nonlinear, and techniques of asymptotics ‘beyond all orders’ are used to determine the (exponentially small as μ → 0) lee-wave amplitude. Comparison with numerical results indicates that the asymptotic theory often remains reasonably accurate even for moderately small values of μ and ε, in which case the (formally exponentially small) lee-wave amplitude is greatly enhanced by nonlinearity and can be quite substantial. Moreover, these findings reveal that the range of validity of the classical linear lee-wave theory (A [Lt ] 1) is rather limited.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 308 , 10 February 1996 , pp. 147 - 170
Copyright
© 1996 Cambridge University Press

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