FULL EULER EQUATIONS FOR WAVES GENERATED BY VERTICAL SEABED DISPLACEMENTS

Abstract

We present a numerical method for simulating the generation and propagation of surface gravity waves by vertical seabed displacements. The cornerstone of our method is the computation of a time-dependent conformal map that incorporates the time-dependent geometry of the seabed in the physical domain and the dynamic wave profile at the free surface, thus enabling us to spectrally integrate the fully nonlinear Euler equations without further restrictions in nonlinearity or dispersion. We validate our numerical method using the linear model for waves generated by small vertical seabed displacements. Comparisons are made between the linear and fully nonlinear models. Finally, we compare the active and passive generation approaches. Solutions of the fully nonlinear Euler equations reveal shortcomings of the passive generation approach; while it yields accurate predictions during the generation stage and propagation of the leading waves, it underestimates the waveheight and wave profiles of subsequent waves.