Coupled modelling of turbidity currents over erodible beds

Abstract

Turbidity currents are significant due to their role in dictating reservoir sedimentation, the safety of deep sea facilities and the formation of submarine morphological features and turbidites. Interactions exist between turbidity current, sediment transport, bed topography and deformation. However, existing mathematical models have ignored these interactions either partly or completely. Therefore these models can be referred to as decoupled or partially coupled models. Uncertainties arising from these simplifications remain unclear. To help address this, the present study advances modelling capability and understanding of turbidity currents in three areas. First, the significance of the interactions is analysed theoretically. Second, a fully coupled mathematical model, which incorporates explicitly the interactions between turbidity current, sediment transport, bed topography and deformation, is developed and tested. Third, the model is applied to submarine turbidity currents and reservoir turbidity currents. It is demonstrated that the model is a viable tool for effective reservoir sediment management and facilitates an improved understanding of the formation of submarine morphological features. Three issues need to be carefully dealt with in turbidity current modelling: 1) the internal hydraulic jumps, 2) the moving current front, -and 3) the irregular topographies in the field. These necessitate a mathematical model being well-balanced and capable of automatically capturing shock waves and tracking the wet/dry front. But to the writer’s knowledge, these aspects have so far not been simultaneously implemented in existing models of turbidity currents. In this study, the finite volume method is used to solve the governing equations and the slope limited centred scheme (SLIC) is employed to estimate the numerical fluxes, rendering the model capable of automatically capturing shock waves. The weighted surface depth gradient method (WSDGM) is implemented in the SLIC scheme, making the model well-balanced and thus applicable to both regular and irregular topographies. The wellbalanced property is demonstrated by successful reproduction of an initially subaqueous static turbidity volume over an irregular hump, as well as the successful application of the model to a real reservoir. The experimentally observed internal hydraulic jump is satisfactorily reproduced by the model, suggesting the ability of the model to accurately capture shock-waves. The accuracy of the model in reproducing key current variables is also demonstrated as against experimental data. The significance of fully coupled modelling is investigated theoretically using the multipletime- scale theory. This is complemented by numerical simulations of self-accelerating turbidity currents. Fully coupled modelling is shown to be critical for refined quality of turbidity current modelling, especially for those cases featuring rapid bed deformation. Decoupled and partially coupled models may be approximately applicable only to turbidity currents with mild bed deformation. Existing understanding of the formation of submarine morphological features is based mainly on indirect back-estimations, which cannot resolve the physical process. Applying the fully coupled model, the formation processes of canyons, channel-levees and lobes are numerically resolved. It is demonstrated that appropriate bed slope and sediment particle size may favour the formation of channel-levee morphology over submarine fans, as larger Richardson number does. Turbidity currents have been generated in a series of water-sediment regulation experiments in the Yellow River, China, aiming to get as much sediment as possible transported to the downstream and therefore reduce reservoir sedimentation. However, post-experiment analyses are mainly in the form of observed data comparisons. Two events of turbidity currents in the Xiaolangdi reservoir are investigated numerically. The advance of the current front and the sediment transport rate are reproduced by the model fairly well. These suggest the present model as a viable tool for determining the timing for operating the bottom outlets, which is critical for effective reservoir sediment management.