Exact Evolution Equations for Surface Waves
- 1 July 1999
- journal article
- research article
- Published by American Society of Civil Engineers (ASCE) in Journal of Engineering Mechanics
- Vol. 125 (7) , 756-760
- https://doi.org/10.1061/(asce)0733-9399(1999)125:7(756)
Abstract
This paper considers surface gravity-capillary waves in an ideal fluid of finite depth and generalizes exact evolution equations for free gravity waves obtained by Dyachenko et al. to those for forced gravity-capillary waves. The model derived here describes the time evolution of the free surface and the velocity potential evaluated at the free surface under external pressure forcing. Two integro-differential equations are written explicitly in terms of these two dependent variables, and no extra step is required to close the system. These equations are solved numerically for the particular case of stationary periodic waves, and the results compared with analogous ones available in the literature.Keywords
This publication has 10 references indexed in Scilit:
- Convergence of a Boundary Integral Method for Water WavesSIAM Journal on Numerical Analysis, 1996
- Analytical description of the free surface dynamics of an ideal fluid (canonical formalism and conformal mapping)Physics Letters A, 1996
- Computations of Steep Gravity Waves by a Refinement of Davies–Tulin’s ApproximationSIAM Journal on Applied Mathematics, 1995
- Nonlinear evolution equations for two-dimensional surface waves in a fluid of finite depthJournal of Fluid Mechanics, 1995
- Generalized vortex methods for free-surface flow problemsJournal of Fluid Mechanics, 1982
- Steep gravity waves in water of arbitrary uniform depthPhilosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1977
- The deformation of steep surface waves on water - I. A numerical method of computationProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1976
- Computer extension and analytic continuation of Stokes’ expansion for gravity wavesJournal of Fluid Mechanics, 1974
- Stability of periodic waves of finite amplitude on the surface of a deep fluidJournal of Applied Mechanics and Technical Physics, 1972
- An exact integral equation for steady surface wavesProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1970