Boussinesq Modeling of Wave Transformation, Breaking, and Runup. I: 1D

Abstract

In this paper, we focus on the implementation and verification of an extended Boussinesq model for surf zone hydrodynamics in two horizontal dimensions. The time-domain numerical model is based on the fully nonlinear Boussinesq equations. As described in Part I of this two-part paper, the energy dissipation due to wave breaking is modeled by introducing an eddy viscosity term into the momentum equations, with the viscosity strongly localized on the front face of the breaking waves. Wave runup on the beach is simulated using a permeable-seabed technique. We apply the model to simulate two laboratory experiments in large wave basins. They are wave transformation and breaking over a submerged circular shoal and solitary wave runup on a conical island. Satisfactory agreement is found between the numerical results and the laboratory measurements.

Hydrodynamic modeling of tsunamis from the Currituck landslide

“…To accurately model these effects it was determined that a grid spacing of 5 m and the fully nonlinear (FNL-EXT) equations were needed. Energy dissipation from wave breaking is employed using an eddy viscosity scheme (Kennedy et al, 2000), though because this is a 1D simulation, the attenuating effect of geometric spreading is not included. Runup was computed at mean sea level, noting that the tidal stage at the time of a tsunami will also influence runup and inundation (Mofjeld et al, 2007).…”

Submarine landslides in the Santa Barbara Channel as potential tsunami sources

“…The wave propagation model is fully nonlinear and able to simulate a wide range of wavelengths not limited to long waves . FUNWAVE is designed to model the physics of breaking waves and runup Kennedy et al, 2000). Geowave takes the tsunami source from TOPICS and inputs this as an initial condition into FUNWAVE at time t o after the landslide begins accelerating.…”

Modeling wave runup with depth-integrated equations

“…To simulate the effects of wave breaking, the eddy viscosity model (Zelt, 1991;Kennedy et al, 2000) is used here. Readers are directed to Kennedy et al (2000) for a thorough description and validation of the breaking model, and the coefficients and thresholds given therein are used for all the simulations presented in this paper.…”

“…Their derivation makes use of the NLSW equations, and thus for consistency the dispersive (l 2 ) terms will be ignored in the numerical simulations for this comparison. The wave and slope parameters for this test case are identical to those used by Madsen et al (1997) and Kennedy et al (2000). A wave train with height 0.006 m and period of 10 s travels in a onedimensional channel with a depth of 0.5 m and a slope of 1:25.…”