Modeling of one-dimensional turbidity currents with a dissipative-Galerkin finite element method

Abstract

A finite element computational algorithm for the solution of one-dimensional, unsteady turbidity currents is presented. The layer-averaged governing equations form a hyperbolic system consisting of three equations, namely continuity and momentum equations for the flow, and mass conservation equation for the sediment. Tracking the front of a propagating turbidity current is akin to the problem of predicting the propagation of a dam-break wave over a dry bed. The standard Galerkin formulation does not give good results when applied to the highly nonlinear flow regime near the front, so the dissipative-Galerkin technique (Petrov-Galerkin technique) which has a selective damping property, is used. The numerical model is applied to the case of a turbidity current developing along a sloping bottom. The computed results compare favorably well against both the relationship proposed by Britter and Linden (1980) to estimate the speed of density currents fronts and the experimental observations made by Altinakar, Graf, and Hopfinger (1990) for weakly-depositional turbidity currents. Satisfactory results are also obtained in both the simulation of an internal hydraulic jump in a turbid underflow and the estimation of the amount of sediment deposited by a turbidity current event.