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Effects of weak wind and damping on Wilton's ripples

Published online by Cambridge University Press:  25 March 1997

KARSTEN TRULSEN  and
CHIANG C. MEI
KARSTEN TRULSEN
Affiliation:
Department of Mathematics, University of Bergen, Johannes Brunsgate 12, N–5008 Bergen, Norway
CHIANG C. MEI
Affiliation:
Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
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Abstract

A model for second-harmonic resonance between two gravity–capillary waves is derived, for the case where weak wind and laminar viscosity are of comparable importance. It is revealed that there exist two threshold wind speeds. For winds weaker than the lower threshold, waves are damped. For winds stronger than the upper threshold, the wave energy becomes unbounded and the spectrum cannot be confined to two resonating harmonics. In the intermediate range there exist steady progressive combination waves of the first and second harmonics. These are Wilton's ripples in equilibrium with wind input and viscous dissipation, and are probably physically observable.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 335 , 25 March 1997 , pp. 141 - 163
Copyright
© 1997 Cambridge University Press

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