Layer-averaged modeling of turbidity currents with a finite element method

A finite element technique has been applied to the hyperbolic system of partial differential equations for a turbidity current flowing in deep ambient water. Since the standard Galerkin method yields spurious oscillations when applied to convection-dominated flows, the dissipative-Galerkin technique which has a selective damping property, is used. In order to track the moving front numerically, a node-adding method is used for the one-dimensional problem of channelized turbidity currents. For two-dimensional non-channelized turbidity currents, a deforming grid generation technique is employed.;Through Fourier analysis, an optimal upwind parameter is derived for the linearized and homogeneous governing equations. However, due to the strong non-homogeneity caused by the water entertainment term in the fluid continuity equation, the upwinding level has to be increased in the present problem. With the help of a numerical experiment, the extra level of upwinding needed is obtained, and this value is found to produce satisfactory results.;The one-dimensional numerical model is applied to laboratory experiments for weakly depositing turbidity currents on mild slopes (Altinakar et al., 1980) and experiments for turbidity currents flowing through an abrupt change in slope (Garcia, 1993). The two-dimensional numerical model is used to stimulate a decelerating-depositional turbidity current and the initiation of a turbidity current by a non-buoyant jet. The computed results illustrate that the present computational algorithms are capable of simulating both the one- and two-dimensional propagations of turbidity currents. Laboratory experiments are also conducted to verify the numerical model and to analyze the the two-dimensional spreading of density currents. Extensive comparisons are made between the numerical solutions and the observed results. A new relationship is developed to describe the two-dimensional spreading of density currents with the help of the experimental observations.