Boussinesq-type model for nearshore wave processes in fringing reef environment

Abstract

The extended lagoons and steep flanks of most fringing reefs produce unique coastal processes that are challenging to numerical wave models developed for continental shelf conditions. This dissertation describes the formulation and validation of a coastal wave model applicable to fringing reef environment. The governing Boussinesq-type equations, which include a continuity and a momentum equation with conserved variables, contain the conservative form of the nonlinear shallow-water equations for shock capturing. The finite volume method with a Godunov-type scheme provides a conservative numerical procedure compatible to the present governing equations. A fifth-order TVD (Total Variation Diminishing) reconstruction procedure evaluates the inter-cell variables, while a directional splitting scheme with a Riemann solver supplies the inter-cell flux and bathymetry source terms in the two-dimensional horizontal plane. Time integration of the governing equations provides the conserved variables, which in turn provide the flow velocities through a linear system of equations derived from the dispersive terms in the momentum equations. The model handles wave breaking through momentum conservation based on the Riemann solver without the use of predefined empirical coefficients for energy dissipation. A series of numerical experiments verify the dispersion characteristics of the model. The computed results show very good agreement with laboratory data for wave propagation over a submerged bar, wave breaking and runup on plane beaches as well as wave transformation over fringing reefs. The model accurately describes transition between supercritical and subcritical flows as well as development of dispersive waves in the processes.