Ge Wei and James T. Kirby and Stephan T. Grilli and R. Subramanya
Graduate student Professor
Associate
Professor Graduate
student
UoD Department
of Civil Eng. University
of Rhode Island
Newark,
DE 19716, USA Narragansett, RI
02882, USA
Abstract :
Fully nonlinear extensions of Boussinesq equations are derived
to simulate surface wave propagation in coastal regions. By using the velocity
at a certain depth as a dependent variable (Nwogu, 1993), the resulting
equations have significantly improved linear dispersion properties in intermediate
water depths when compared to standard Boussinesq approximations. Since
no assumption of small nonlinearity is made, the equations can be applied
to simulate strong wave interactions prior to wave breaking. A high order
numerical model based on the equations is developed and applied to the
study of two canonical problems: solitary wave shoaling on slopes and undular
bore propagation over a horizontal bed. Results of the Boussinesq model
with and without strong nonlinearity are compared in detail to those of
a boundary element solution of the fully nonlinear potential flow problem
developed by Grilli et al. (1989). The fully nonlinear variant of
the Boussinesq model is found to predict wave heights and particle kinematics
more accurately than the standard approximation, while phase speed predictions
are not uniformly improved.