Boussinesq-type model for energetic breaking waves in fringing reef environments

The steep offshore slope and abrupt transition to a shallow lagoon are conducive to formation of energetic breaking waves in fringing reef environments. This paper describes an extension of a one-dimensional, shock-capturing Boussinesq-type model to account for these processes in two dimensions and the numerical formulation to facilitate adaptive time integration and code parallelization. The governing equations contain the conservative form of the nonlinear shallow-water equations to capture shock-related hydraulic processes. The finite volume method with a Godunov-type scheme provides a compatible, conservative numerical procedure. A two-dimensional TVD (Total Variation Diminishing) reconstruction procedure evaluates the flow variables on either side of the cell interface, while a Riemann solver supplies the flux and bathymetry source terms at the interface. A well-balanced scheme eliminates depth-interpolation errors in the domain and preserves continuity across moving boundaries over irregular topography. Time integration of the governing equations evaluates the conserved variables, which in turn provide the horizontal velocity components through systems of linear equations corresponding to series of one-dimensional problems. The application of the model to fringing reef environments is validated with laboratory experiments performed at Oregon State University as well as field data collected in Hawaii. The model describes the flux-dominated wave breaking processes through the Riemann solver without predefined empirical energy dissipation and reproduces transitions between sub and supercritical flows as well as development of dispersive and infra-gravity waves in the processes.

► Development of conservative Boussinesq-type model for breaking waves over reef bathymetry.
► Efficient and robust mathematical and numerical formulation is outlined.
► Model is validated with laboratory and field data.