Higher-Order Modeling of Water Waves Generated by Submerged Moving Disturbances

In this paper, a recently derived (Zhou, 2008) fully nonlinear and higher-order dispersive Boussinesq-type model for wave generation and propagation is presented. This new model is an extension of the wave propagation model by Gobbi and Kirby (1999) and Gobbi et al. (2000) to include the time-varying seabed bathymetry. The resulting new version retains the 4th-order approximation of the dispersion relation and the velocity distribution in the vertical direction, and extends the application to both water wave propagation and wave generation by seabed disturbances such as submarine landslides. The model equations are solved numerically through a higher-order finite difference scheme. To examine the validity of the new model and the improvement due to the higher-order extensions, numerical simulations of two wave generation cases are carried out based on the new 4th order model and an existing lower order Boussinesq model. The results show that the higher order model provides the more accurate prediction for the generated waves, especially those in the trailing region of shorter wavelengths where the traditional lower order Boussinesq model becomes much less accurate.