A two--dimensional boundary integral equation model with the mixed Eulerian-Lagrangian approach was presented to solve the problem of water wave generation, propagation, and run-up. A composite uniform cubic B-spline curve fitting technique was applied on the free surface with the Lagrangian approach. The accuracy of the free surface computation was up to O(Delta t^2). A modified Sommerfeld-type radiation boundary condition was presented to reduce the computational domain. The radiation boundary was tested by using solitary waves and non--permanent monochromatic wave trains with kh = 0.28 to 1.31. Very good results were obtained for wave height H / h < 0.4. The effect of bottom friction was considered via the boundary layer approximation. Numerical results showed that bottom friction reduces wave heights by a maximum of 2.5% for the long waves with kh = 0.28.
A numerical wave tank was proposed to study the the evolution of monochromatic wave trains in shallow and intermediate water depth. Experiments were conducted to compare with the numerical results. The good agreement shows that the potential theory is valid in this region. The results also verified the conclusion in Madsen et al. (1970) which states that there will be a region of cnoidal waves. The importance of the Ursell number was also confirmed.
Waves generated by submarine landslides were studied by assuming the landslides are incompressible viscous fluids. The viscous flow was solved by using the implicit finite-difference method. The governing equations derived from long-wave approximation show that the term coupling water waves and landslide motion is very small and of O(epsilon). The landslide generated waves have an initial shape similar to an N wave with a crest moving in the off-shore direction. The run-up height is much smaller than the run--down height. The 1975 Kitimat submarine landslides were simulated and reasonable results were obtained. The results of the large scale landslides having large Reynolds numbers show that the viscosity of the slide was not an important factor in affecting the slide motion; the dominant factor of the slide property is the density of the slide.