FM26S_11468:Thu:1505:309
XXI International Congress of Theoretical and Applied Mechanics
Warsaw, Poland, August 15-21, 2004

Evolution of Packets of Surface Gravitywaves over Smooth Topography

Eugene S. Benilov, Jason D. Flanagan, Colm P. Howlin
University of Limerick, Ireland


Weakly nonlinear packets of surface gravity waves over topography are governed by a nonlinear Schroedinger equation with variable coefficients (Djordjevic & Redecopp 1978). Using this equation and assuming that the horizontal scale of topography is much larger than the width of the packet, we show that, counter-intuitively, the amplitude of a shoaling packet decays, while its width grows. Such behaviour is a result of the fact that the coefficient of the nonlinear term in the topography-modified Schroedinger equation decreases with depth. Furthermore, there exists a critical depth, where this coefficient changes sign: if the packet reaches this depth, it disintegrates.



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