Energy of water waves induced by submarine landslides

Water waves generated by submarine landslides may constitute a serious haza rd for coastal population and environment. These masses may be giant, as do cumented by several examples in recent history and by numerous geological t races of paleo-events. A theoretical investigation on wave generation and w ave energy is performed here by using a model that is based on some simplif ying assumptions. The landslide is treated as a rigid body moving underwate r according to a prescribed velocity function. Water waves are governed by the shallow-water wave equations, where water velocity is constant through the water layer and vertical velocity is negligibly small. Geometrically si mple basins are considered with either constant depth or constant slope, si nce attention is focused on the fundamental characteristics of the generati on process. Analytical 1-D solutions as well as 1-D and 2-D numerical resul ts obtained by means of a finite-element model are used to gain understandi ng of the energy transfer from a moving body to the water. From the 1-D exa mples, it is found that if slide duration is sufficiently long, water usual ly gains energy in the form of waves until a saturation point is reached, w hen body motion is no longer capable of producing a net transfer of energy from the rigid body to water. Finite-duration motions of a body moving at c onstant speed along a flat ocean floor can be used as canonical examples, s ince bottom slopes cannot significantly change the generated wave pattern. Typically, two trough-crest systems are developed that travel in opposite d irections, with the leading crest in the direction of the slide and the lea ding trough toward the other direction. The amplitude of the former is gene rally higher, with amplitude controlled by the Froude number (ratio of body velocity to long waves phase celerity) and wavelength dictated by landslid e length. Generation and propagation of 2-D cases show a more complicated p attern, since lateral radiation plays an important role. Some of the featur es present in the 1-D models are observed in 2-D wavefields, however substa ntial differences arise. The most significant difference is that no energy saturation takes place in 2-D, since the body transfers energy to the water as long as it moves.