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Transverse instability of solitary-wave states of the water-wave problem

Bridges, T. J. (2001) Transverse instability of solitary-wave states of the water-wave problem Journal of Fluid Mechanics.


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Transverse stability and instability of solitary waves correspond to a class of perturbations that are travelling in a direction transverse to the direction of the basic solitary wave. In this paper we consider the problem of transverse instability of solitary waves for the water-wave problem, from both the model equation point of view and the full water-wave equations. A new universal geometric condition for transverse instability forms the backbone of the analysis. The theory is first illustrated by application to model PDEs for water waves such as the KP equation, and then it is applied to the full water-wave problem. This is the first theory proposed for transverse instability of solitary waves of the full water-wave problem. The theory suggests the introduction of a new functional for water waves, whose importance is suggested by the mathematical structure. Without explicit calculation, the theory is used to argue that the basic class of solitary waves of the water-wave problem, which bifurcate at Froude number unity, are likely to be stable to transverse perturbations, even at large amplitude.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
Bridges, T.
Date : 1 July 2001
Additional Information : Published in the Journal of Fluid Mechanics (2001), 439:255-278. Copyright © 2001 Cambridge University Press. Reprinted with permission. Click here to visit the journal site.
Depositing User : Mr Adam Field
Date Deposited : 27 May 2010 14:40
Last Modified : 08 Nov 2013 10:18

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