Weihang Sun

In this work, we propose a comprehensive two‐layer depth‐averaged model to study the dynamic behavior of grain‐fluid mixtures, which considers the granular dilatancy effects and the different frictional rheologies of grains in different states. Unlike single‐phase flows, not only the interaction between granular and fluid phases significantly influence the dynamics of mixtures, but also the phase separation, so that different flow regimes can occur. These include five different possible regimes: two‐layer regimes of (a) under‐saturated mixture and (b) over‐saturated mixture as well as single‐layer regimes of (c) saturated mixture, (d) pure grains and (e) pure fluid. Most depth‐averaged models in previous studies have considered only one of these flow regimes. The present model is an improved and integrated version of these depth‐averaged models. Taking into account that the pure grains and pure fluid in the upper layer, which occur in the regimes of the under‐saturated and over‐saturated grain‐fluid mixtures, respectively, exhibit different flow features than in the lower layer of the saturated mixture, we use a two‐phase two‐layer depth‐averaged model to describe these regimes. This proposed model is possibly the first to employ a two‐layer structure to describe all possible different flow regimes simultaneously. The proposed model is then solved numerically using a high‐resolution central‐upwind scheme and shows its ability to handle different flow regimes. To demonstrate the robustness of the numerical implementation and to evaluate the performance of the model, the numerical results are compared with several experiments reported in the literature, showing a certain qualitative agreement.

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.