A Depth‐Averaged Description of Submarine Avalanche Flows and Induced Surface Waves. Issue 4 (15th April 2023) - Sun, W.; Meng, X.; Wang, Y.; Hsiau, S. S.; You, Z.
Abstract: 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. Plain Language Summary: Developing an accurate and rigorous model to describe the motion of submarine landslides and the evolution of the induced water wave remains a challenge to date. Existing models usually simplify the submarine mass as a sling box or a deformable rheological material which is unable to interpret certain fast‐moving and some slow‐moving granular flows that differ only in their compactness. In this paper, the existing models are improved by taking account of the dilatancy effects of the particles. Numerical results of underwater granular collapse show that the predictions of the temporal evolution of the thickness profiles and the final deposit morphology using the current model are in better agreement with experiments compared to the existing models. The present model also provides a better prediction in the wave profiles induced by submarine landslides, which makes the present theory very promising to investigate natural geophysical flows in the future. Key Points: A depth‐averaged model is presented, which considers excess pore fluid pressure and fluid mass transfer across the avalanche surface A robust numerical method is used, so that the computed solution is insensitive to the way nonconservative products are discretized Significant improvements in the prediction of the grain thickness profiles and the free‐surface waves are found compared with existing models