NUMERICAL MODELING OF AN UNDERWATER BINGHAM PLASTIC MUDSLIDE AND THE WAVES WHICH IT GENERATES

Underwater landslides are a common source of tsunamis in coastal areas . Theoretical and experimental studies on this problem, however, are s carce because of the difficulties in modeling and observing a submarin e slide and the associated tsunami. To study this problem, we present a numerical model that simulates the coupling of a Bingham plastic mud slide on a gentle uniform slope with the surface waves which it genera tes. A formulation of the dynamics of the problem is presented, where the landslide is treated as an incompressible Bingham plastic flow and the water motion is assumed irrotational. The long-wave approximation is adopted for both water waves and the mudslide. Dispersion of waves and potential turbulent mixing are not considered. The resulting diff erential equations are solved by a finite difference method. We presen t the numerical results for successive profiles of the mud surface, th e horizontal velocity distributions of the slide, the evolution of the surface elevations, and the distributions of the particle velocity of the water motion. Three major parameters dominate the magnitude of th e waves (if the volume of the mud is fixed): the density of mud, the y ield stress of the mud, and the depth of water at the mudslide site. B ecause of the yield stress, the slides stop on the slope when the shea r stress exerted on the bottom become smaller than the yield stress. T he Bingham plastic behavior of the mud significantly reduces the exten t and the speed of the mudslide and also the magnitude of the surface waves generated. Comparison of the solution of the Bingham plastic mud slide model with a snow flow test is presented. The solution of a visc ous fluid model has been derived as a special case of the present solu tion.