Extended Fourth-Order Depth-Integrated Model for Water Waves and Currents Generated by Submarine Landslides

In this paper, a preexisting higher-order depth-integrated wave propagation model is extended to include a moving seabed. As a result, the extended model can be applied to both wave propagation and the dynamic process of wave generation by a seabed disturbance such as a submarine landslide. The model has the linear dispersion relation in a form of (4,4) Padè approximant, and approximates the water velocity profiles along the water depth with a fourth-order polynomial of the vertical coordinates. The fourth-order model is aimed at extending the validity of the lower-order depth-integrated models from long waves to both long and shorter waves, as well as improving the approximation of the velocity field from the second order to the fourth order. Laboratory experiments are carried out in a wave flume to study wave generation by a submerged landslide model. Both water waves and water velocities are measured by using resistance-type wave gauges and a particle image velocimetry. The experimental data are then compared with the predicted wave height and water current based on the new model and two existing lower-order Boussinesq-type models. The results clearly show that the new model predicts the fluid velocity more accurately and is also able to predict the shorter trailing waves very well where the traditional Boussinesq model may be inadequate, thus validating the improvement provided by the fourth-order model.