Two-dimensional depth-averaged two-layer flow model for well-mixed reservoirs

Abstract

A mathematical model of two-dimensional two-layer flow has been developed for computation of flow circulation in a reservoir. The flow equations are solved for each layer consecutively. The flow region is divided by a reference surface in which the friction coefficient is constant and its shear stresses described by the quadratic friction law. The vertical mass exchange between the upper and lower layers is assumed to be small and negligible. The momentum exchange between the two layers is accounted for by the internal shear stress along the reference surface. The effect of stratified flow due to density difference or temperature gradients are not considered. The model was used to investigate the flow circulation in a hypothetical reservoir. The effect of individual flow boundary conditions were studied. It has been found that 1) the internal shear stress at the reference line are important for the occurrence of flow circulation in the lower layer ; 2) the peizometric gradient also contributes to the flow pattern in the lower layer ; 3) the bed resistance has small effect on the circulation in the lower layer ; 4) the reference surface fluctuates during the iteration process and becomes stationary when the steady state convergence has been reached.