Finite Element Model of 2-D Stratified Flow

A finite element model for the study of hydrodynamics and salt transport in partially-mixed estuaries is presented. The model is based on the laterally integrated time varying equations of motion, continuity and conservation of salt. The Boussinesq approximation is applied to the resulting two-dimensional equations and a simple equation of state is used to relate salinity to density. Although a rigorous mathematical proof cannot be given it is heuristically postulated that the correct boundary conditions, defining a well-posed problem, must consist of applied stresses or strain rates in cases with internal (Reynolds) stresses included. Without the internal stresses the pressure or the normal strain rate only can be prescribed. A simple application demonstrates the ability of this model to accurately represent the moving surface. Another example illustrates the significance of ocean boundary conditions on the internal solution.