Evolution equation for short surface waves on water of finite depth
Nenhuma Miniatura disponível
Data
2009-08-15
Autores
Artiles, W. [UNESP]
Kraenkel, Roberto André [UNESP]
Manna, M. A.
Título da Revista
ISSN da Revista
Título de Volume
Editor
Elsevier B.V.
Resumo
We address the question of determining the evolution equation for surface waves propagating in water whose depth is much larger than the typical wavelength of the surface disturbance. We avoid making the usual approximation of supposing the evolution to be given in the form of a modulated wave-packet. We treat the problem by means of a conformal transformation allowing to explicitly find the Dirichlet-to-Neumann operator for the problem together with asymptotic expansions in parameters measuring the nonlinearity and depth. This allows us to obtain an equation in physical variables valid in the weakly nonlinear, deep-water regime. The equation is an integro-differential equation, which reduces to known cases for infinite depth. We discuss solutions in a perturbative setting and show that the evolution equation describes Stokes-like waves. (C) 2009 Elsevier B.V. All rights reserved.
Descrição
Palavras-chave
Water-waves, Deep-water asymptotics, Conformal mapping, Stokes waves
Como citar
Physica D-nonlinear Phenomena. Amsterdam: Elsevier B.V., v. 238, n. 17, p. 1821-1825, 2009.