Generation of internal and surface waves by seafloor movement in a two layer fluid system

Internal and surface waves generated by the deformations of the solid bed in a two layer fluid system of infinite lateral extent and uniform depth are investigated. An integral solution is developed for an arbitrary bed displacement on the basis of a linear approximation of the complete description of wave motion using a transform method (Laplace in time and Fourier in space) analogous to that used to study the generation of tsunamis by many researchers. The theoretical solutions are presented for three interesting specific deformations of the seafloor; the spatial variation of each seafloor displacement consists of a block section of the seafloor moving vertically either up or down while the time-displacement history of the block section is varied. The generation process and the profiles of the internal and surface waves for the case of the exponential bed movement are numerically illustrated, and the effects of the deformation parameters, densities and depths of the two layers on the solutions are discussed. As expected, the solutions derived from the present work include as special cases that obtained by Kervella et al. [Theor Comput Fluid Dyn 21:245-269, 2007] for tsunamis cased by an instantaneous seabed deformation and those presented by Hammack [J Fluid Mech 60:769-799, 1973] for the exponential and the half-sine bed displacements when the density of the upper fluid is taken as zero.

Numerical Simulation of Waves Generated by Seafloor Movements

Waves generated by vertical seafloor movements are simulated by use of a fully nonlinear two-dimensional numerical wave tank. In the source region, the seafloor lifts to a designated height by a generation function. The numerical tests show that file linear theory is only valid for estimating the wave behaviors induced by the seafloor movements with a small amplitude, and the fully nonlinear numerical model should be adopted in the simulation of the wave generation by the large amplitude seafloor movements. Without the background surface waves, many numerical tests on the stable maximum elevations eta(max)(0) are carried out by both the linear theory and the fully nonlinear model. The results of two models are compared and analyzed. For the fully nonlinear model, the influences of the amplitudes and the horizontal lengths on eta(max)(0) are stronger than that of the characteristic duration times. Furthermore, results reveal that there are significant differences between the linear theory and the fully nonlinear model. When the influences of the background surface waves are considered, the corresponding numerical analyses reveal that with the fully nonlinear model the eta(max)(0) near-linearly varies with the wave amplitudes of the surface waves, and the eta(max)(0) has significant dependences on the wave lengths and the wave phases of the surface waves. In addition, the differences between the linear theory and the fully nonlinear model are still obvious, aid these differences are significantly affected by The wave parameters of the background surface waves, such as the wave amplitude, the wave length and the wave phase.