Journal of Fluid Mechanics

A fully nonlinear Boussinesq model for surface waves. Part 1. Highly nonlinear unsteady waves

Ge  Wei a1, James T.  Kirby a1, Stephan T.  Grilli a2 and Ravishankar  Subramanya a2
a1 Center for Applied Coastal Research, University of Delaware, Newark, DE 19716, USA
a2 Department of Ocean Engineering, University of Rhode Island, Narragansett, RI 02882, USA

Article author query
wei g   [Google Scholar] 
kirby jt   [Google Scholar] 
grilli st   [Google Scholar] 
subramanya r   [Google Scholar] 


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, phase speeds and particle kinematics more accurately than the standard approximation.

(Published Online April 26 2006)
(Received July 21 1994)
(Revised January 10 1995)

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