Three-Dimensional Modeling of Tsunami Generation Due to a Submarine Mudslide

Abstract

Submarine landslides are a common cause of tsunamis in coastal and estuarine areas. To study this phenomenon, a numerical model is developed to simulate tsunami generation due to a viscous mudslide on a gentle uniform slope. A formulation of the dynamics of the problem is presented, where the mudslide is treated as an incompressible three-dimensional viscous flow. Seawater is treated as an inviscid fluid, and the water motion is assumed irrotational. The long-wave approximation is adopted for both water waves and the mudslide. The resulting differential equations are solved by a finite-difference method. The focus of this paper is to examine the effects of the longitudinal spreading as well as the transversal spreading of the slide upon surface wave generation, and the spreading of water waves sideways. Three-dimensional pictures are presented for successive profiles of the mud surface, the horizontal velocities of the mudslide, the evolution of the surface elevations, and the velocities of the water motion. Comparisons of the present three-dimensional calculations with previously published two-dimensional results indicate small differences for large length/width ratios for a small time after the initiation of the slide. Generally, however, the water surface profiles deviate significantly from the two-dimensional results. Adequate simulations thus require accurate representation of the aspect ratio of the sliding mass.