Tsunami Excitation by Submarine Slides in Shallow-water Approximation

Abstract

— Landslide-induced tsunamis are receiving increased attention since there is evidence that recent large devastating events have been caused by underwater mass failures. Normally, numerical models are used to simulate tsunami excitation, most of which are based on shallow water, known also as long wave, approximation to the full equations of hydrodynamics. Analytical studies may handle only simplified problems, but help understand the basic features of physical processes. This paper is an analytical investigation of long-water waves excited by rigid bodies sliding on the sea bottom, based on the shallow-water approximation, which is here derived by properly scaling Euler equations for an inviscid, incompressible and irrotational ocean. In one-dimensional (1-D) cases (where motion depends only on one horizontal coordinate), under the further assumptions of small-height slide, which permits the recourse to linear theory, and of flat ocean floor, a solution for arbitrary body shape and velocity is deduced by applying the Duhamel theorem. It is also shown that this theorem can be advantageously used to obtain a general solution in case of a non-flat ocean floor, when the sea bottom follows a special power law, that can be adapted to study reasonable bottom profiles. The characteristics of the excited tsunamis are then evaluated by computing solutions in numerous examples, with special focus on wave pattern and wave evolution. The energy of the wave system is shown to depend on time: it grows expectedly in the initial phase of tsunami generation, when the moving body transfers energy to the water, but it may also diminish later, implying that a certain amount of energy may pass back from water waves to the slide.