Well-balanced two-dimensional coupled modelling of submarine turbidity currents

Submarine turbidity currents may wreak havoc on deep sea facilities and also affect the formation of many morphological features, which are closely linked to hydrocarbon reserves. Yet most previous understandings are based on the analyses of geological and geophysical data or decoupled modelling. Here a two-dimensional coupled mathematical model for turbidity currents over erodible beds is developed. The governing equations are built upon the complete layer-averaged mass and momentum conservation laws. The well-balanced slope limiter centred scheme is deployed, which facilitates a reasonable balance between the flux gradients and the bed source terms. This renders the model applicable to both regular and irregular topographies. The coupled model is verified against both one- and two-dimensional experimental turbidity currents. When applied to turbidity currents near a submarine canyon–-fan transition and over submarine fans, coupled modelling is found to be critical, which incurs negligible increase in the computational cost. Computational case studies demonstrate that bed slope, sediment particle size and upstream boundary condition are key factors dictating the formation of submarine channel–levee morphology. Appropriate bed slope and sediment particle size as well as larger inlet Richardson number may favour formation of submarine channel–levee morphology.