A higher-order depth-integrated model for water waves and currents generated by underwater landslides

Abstract

A joint theoretical, numerical and experimental study is carried out to develop an improved wave model for predicting water waves and fluid current generated by underwater landslides. In the theoretical study, a fully nonlinear and higher-order dispersive depth-integrated hydrodynamic model by Gobbi and Kirby (1999) and Gobbi et al (2000) is extended to include the time variation in bathymetry. Upon this extension, the new model can be applied to simulate both wave propagation and the dynamic process of wave generation. by a submerged moving object such as an underwater landslide. Compared with the lower-order (first- or second- order) traditional long wave models, the higher-order model improves the modeling of the dispersive effect to the fourth-order, thus extending the validity of the wave model from long waves (wavelength-to-water depth ratio larger than 10) to shorter waves (wavelength comparable to the water depth). In addition, it also improves the approximation of the vertical fluid velocity profile from the second-order parabolic assumption to a fourth-order polynomial function for more accurate prediction of the fluid current induced by waves: A finite difference scheme is applied to solve the model equations in one spatial dimension. The new model developed in this thesis is derived independently from the fourth order model by Ataie-Ashtiani and Najafi-Jilani (2007) which is similar but differs from the new model in this thesis. Experiments also are carried out in a wave flume in the Hydraulics Laboratory of the Department of Civil and Environmental Engineering at the University of Hawaii. Waves are generated by rigid landslide models sliding down an incline with adjustable slopes. The wave elevation is measured by resistance-type wave gauges and the fluid velocity with particle image velocimetry (PIV). The present higher-order model then is applied to simulate the experimental cases and the numerical results are compared with the experimental data as well as with the results based on two existing lower -order wave models. The results show that the present higher-order model agrees with the experimental measurement better for both the wave elevation and especially the fluid velocity induced by the waves and the landslide motion. Most existing studies focus on wave measurement and prediction. This study is among the first to conduct experiments to measure the landslide induced velocity field and compare the measured velocity with the predicted results. Tsunami sensitivity to landslide features also is investigated through numerical experiments. Empirical equations are derived for predicting the tsunami wave amplitude and water velocities under the waves, based on the numerical experiments. With its improved wave dispersion relation and more accurate prediction for the fluid velocity field, the new model developed in this study can be useful to study a wider range of coastal and hydraulic engineering problems including landslide-generated tsunamis and the associated fluid current which is important in the study of sediment transport and seabed erosion during a tsunami attack. Other problems that can also apply the present higher-order model may include prediction of water surface evolution for open channel flows over different bottom disturbances, and surface waves generated by submerged moving vehicles in the shallow ocean in naval applications.