A Depth-Averaged Description of Submarine Avalanche Flows and Induced Surface Waves

This paper develops a depth-averaged theory to investigate submarine landslides and resulting water waves. The problems here consist of a pure fluid regime and a mixture regime of grains and fluid. Both regimes separate from one another by an interface, which is a material surface for grains. While the downslope velocities of the both phases are assumed to be identical in the mixture regime, the velocity shear causes a rearrangement of grains, which induces a vertical relative motion between the phases. The established theory consists of five coupled conservation equations, which describe the evolution of the pure fluid thickness, the mixture thickness, the solids volume fraction, and depth-averaged velocities. To handle nonconservative products emerging in the equations, a new coordinate system is introduced to rewrite the equation system in an equivalent form, so that numerical solutions are insensitive to the choice of discretization of nonconservative products, which enables us to accurately characterize the dynamic behaviors of particles in the collapse experiments of underwater particles and describe free-surface wave profiles. It is shown that the computed results are in good agreement with the experiments reported in previous literatures.