The coupling of a submarine slide and the surface waves which it generates

Abstract

Underwater landslides are a common source of small‐scale tsunamis in coastal areas. They have been the object of only a few theoretical and experimental studies. A numerical model is developed to study the coupling of a submarine landslide and the surface waves which it generates. A formulation of the dynamics of the problem is presented, where the landslide is treated as the laminar flow of an incompressible viscous fluid and the water motion is assumed irrotational. Long‐wave approximation is adopted for both water waves and the mudslide. The resulting differential equations are solved by a finite‐difference method. We present the numerical results which contrast the behavior of the mud flow under a fixed surface, in the presence of one‐way coupling (bottom deformations affect the free surface), and with full coupling (surface pressure gradients react on the mud flow). It is found that three main waves are generated by a landslide starting from rest on a gentle uniform slope. The first wave is a crest which propagates away from the mudslide site into deeper water; this crest is followed by a trough in the form of a forced wave which propagates with the speed of the mudslide front. The third wave is a relatively small trough which propagates shoreward. Two major parameters dominate the interaction between the slide and the waves it produces: the density of sliding material and the depth of water at the mudslide site. The two‐way interactions are significant for the cases of a smaller mud density and shallower waters. For the cases of larger mud density and shallower waters, the two‐way interactions are small, but the waves generated are very large. For larger initiation depth of the mudslide, the interactions are weak and the waves generated are small. We also examined the possibility of a resonance between the slide and the waves. Our numerical results indicate that a resonance is not expected in many practical cases.