On shoaling properties of enhanced Boussinesq models
Résumé
In this paper, we investigate the nonlinear properties of Boussinesq models.
In particular, we consider the wave shoaling obtained in physical regimes which
go from linear to weakly nonlinear, to the wave breaking limit. For a given asymptotic
accuracy in terms of dispersion and nonlinearity, we consider two families of
models: the first depending on derivatives of the velocity, the second on derivatives
of the volume flux. Ww show that, while linear dispersion and linear shoaling characteristics
are strongly dependent on the type of dispersive terms introduced, when
approaching the nonlinear regime the only influencing factor is whether the model is
in amplitude-velocity of amplitude-flux form. We investigate these two alternative
formulations of several known models, and propose a new model with a compact
differential form, and the same linear characteristics of the model of Nwogu. The
nonlinear shoaling properties of the models are investigated numerically showing
that inside one given family, all the models have almost identical behaviour.