On the nonlinear behaviour of Boussinesq type models: Amplitude-velocity vs amplitude-flux forms

摘要: In this paper we consider the modelling of nonlinear wave transformation by means weakly Boussinesq models. For a given couple linear dispersion relation-linear shoaling parameter, show how to derive two systems PDEs differing in form dispersive operators. particular, within same asymptotic accuracy, these operators can either be formulated derivatives velocity, or terms flux. first case speak amplitude-velocity model, second amplitude-flux form. We examples couples for several relations, including new variant model Nwogu (J. Waterway, Port, Coast. Ocean Eng. 119, 1993). then show, both analytically and numerical tests, that while small amplitude waves accuracy relations is fundamental, when approaching breaking conditions it only equations which determines behaviour particular shape height waves. regime thus find types behaviours, whatever relation coefficient. This knowledge has tremendous importance considering use models conjunction with some detection dissipation mechanism.