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A Lagrangian for water waves

Balk, A. M. (1996) A Lagrangian for water waves. Physics of Fluids, 8 (2). pp. 416-420. ISSN 1070-6631. http://resolver.caltech.edu/CaltechAUTHORS:BALpof96

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Abstract

A Lagrangian for strongly nonlinear unsteady water waves (including overturning waves) is obtained. It is shown that the system of quadratic equations for the Stokes coefficients, which determine the shape of a steady wave (discovered by Longuet-Higgins 100 years after Stokes derived his system of cubic equations) directly follows from the canonical system of Lagrange equations. Applications to the investigation of the stability of water waves and to the construction of numerical schemes are pointed out.


Item Type:Article
Additional Information:©1996 American Institute of Physics. (Received 25 July 1995; accepted 30 October 1995) This paper arose from discussions with Professor P. G. Saffman. I am greatly indebted to him for these valuable discussions, his advice, and encouragement. I am grateful to Professor D. I. Meiron for stimulating discussions, which suggested the second question in the motivation of this paper (see the Introduction).
Subject Keywords:ACTION INTEGRAL; HAMILTONIAN FUNCTION; INCOMPRESSIBLE FLOW; INSTABILITY; LAGRANGIAN FUNCTION; VARIATIONAL METHODS; WATER WAVES; WAVE EQUATIONS; WAVE PROPAGATION
Record Number:CaltechAUTHORS:BALpof96
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:BALpof96
Alternative URL:http://dx.doi.org/10.1063/1.868795
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:3363
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:01 Jun 2006
Last Modified:26 Dec 2012 08:54

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