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Linear instability mechanisms for sand wave formation

Published online by Cambridge University Press:  25 June 2000

NATALIA L. KOMAROVA  and
SUZANNE J. M. H. HULSCHER
NATALIA L. KOMAROVA
Affiliation:
Department of Mathematics, University of Warwick, Coventry, CV4 7AL, UK Institute for Advanced Study, School of Mathematics, Einstein Dr., Princeton, NJ 08540, USA
SUZANNE J. M. H. HULSCHER
Affiliation:
Department of Civil Engineering, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
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Abstract

A height- and flow-dependent model for turbulent viscosity is employed to explain the generation of sand waves in tidal seas. This new model resolves the problem of excitation of very long waves in sand wave formation, because it leads to damping of the long waves and gives a finite separation between the most excited mode and the zero mode. For parameters within their physically realistic ranges, a linear analysis of the resulting system yields a first excited mode whose wavelength is similar to the characteristic wavelength of sand waves observed in nature. The physical mechanism of sand wave formation as predicted by the new model is explained in detail. The dispersion relation obtained can be the starting point for a weakly nonlinear analysis of the system.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 413 , 25 June 2000 , pp. 219 - 246
Copyright
© 2000 Cambridge University Press

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