K. Nadaoka et al., A FULLY DISPERSIVE WEAKLY NONLINEAR MODEL FOR WATER-WAVES, Proceedings - Royal Society. Mathematical, physical and engineering sciences, 453(1957), 1997, pp. 303-318
Citations number
16
Journal title
Proceedings - Royal Society. Mathematical, physical and engineering sciences
A fully dispersive weakly nonlinear water wave model is developed via
a new approach named the multiterm-coupling technique, in which the ve
locity field is represented by a few vertical-dependence functions hav
ing different wave-numbers. This expression of velocity, which is appr
oximately irrotational for variable depth, is used to satisfy the cont
inuity and momentum equations. The Galerkin method is invoked to obtai
n a solvable set of coupled equations for the horizontal velocity comp
onents and shown to provide an optimum combination of the prescribed d
epth-dependence functions to represent a random wave-field with divers
ely varying wave-numbers. The new wave equations are valid for arbitra
ry ratios of depth to wavelength and therefore it is possible to recov
er all the well-known linear and weakly nonlinear wave models as speci
al cases. Numerical simulations are carried out to demonstrate that a
wide spectrum of waves, such as random deep water waves and solitary w
aves over constant depth as well as nonlinear random waves over variab
le depth, is well reproduced at affordable computational cost.