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Three‐dimensional travelling gravity‐capillary water waves
Author(s) -
Groves M. D.
Publication year - 2007
Publication title -
gamm‐mitteilungen
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.239
H-Index - 18
eISSN - 1522-2608
pISSN - 0936-7195
DOI - 10.1002/gamm.200790013
Subject(s) - citation , mathematical sciences , mathematics , computer science , library science , mathematics education
The classical water-wave problem concerns the irrotational flow of a perfect fluid of unit density subject to the forces of gravity and surface tension. The fluid motion is described by the Euler equations in a domain bounded below by a rigid horizontal bottom {y =-h} and above by a free surface which is described as a graph {y = (x, z, t)}, where the function depends upon the two horizontal spatial directions x, z and time t. In terms of an Eulerian velocity potential f(x, y, z, t) the mathematical problem is to solve the equations