Improve layer-averaged turbidity current model using density based flow-sediment-bed coupled equation system

The field-scale numerical simulation of the turbidity currents relies heavily on the layer-averaged models after the pioneering work by G. Parker, M.H Garcia, and others. Considering the flow is generally dilute, these models, including revised fully coupled models (e.g. Hu et al.'s model), employ the Boussinesq approximation and also assume that the water phase density in the turbidity flow is the same as the ambient liquid and its value keeps constant. Recently, field observations find that the concentration profile along the depth is far from uniform and the concentration near the bed is so large that the acoustics signal could not penetrate. Modelling these phenomena demands multi-layer models which can handle relatively high sediment concentration and complex ambient liquid. Here, we present our two-dimensional single-layer-averaged flow-sediment-bed coupled numerical model using the density of the mixture as a conservative variable instead of sediment concentration. The erosion, deposition, entrainment, and friction are considered using previous sub-models. The numerical model is developed based on the open source code, Basilisk, ensuring well-balanced and positivity-preserving properties. An adaptive spatial discretization is used, which allows multi-level refinement. The numerical scheme has a relatively high computational efficiency compared with models based on the Cartesian mesh. A hypothetical case based on a true large-scale landform (the Moroccan turbidite system, offshore NW Africa) is studied to test the availability of the model. The model works fine for various cases and some difference, especially the position of the hydraulic jump, is observed compared with the previous model. This model could be a step to a practical multi-layer-averaged field-scale model for the mudflow and the turbidity flow.