NUMERICAL MODELING OF DISPERSION IN STRATIFIED WATERS

Abstract

A numerical model is developed for the quantitative description of the dispersion process in a two-layer system which represents an approximation for a natural coastal water body during the summer season when a distinct thermocline usually exists. The formulation is based on the convection-diffusion equation, vertically integrated between the layer boundaries. Layer velocities and thicknesses are assumed to be obtained from a separate hydrodynamic model. The quantification of the physical processes of entrainment and mixing through the density interface as well as the horizontal dispersion mechanisms is discussed. The finite element method is chosen for numerical implementation because of its flexibility in grid layout and easier handling of spatial and temporal variability. Triangular elements with linear interpolation functions are used for the spatial discretization, while a simple implicit iterative scheme based on the trapezoidal rule is employed for time integration. The method is shown to be unconditionally stable, for an arbitrary grid and both one- and two-layer problems, when there is no iteration and the parameters are constant. General convergence criteria required by the iteration procedure are developed and expressed in terms of the basic parameters of the problem and are subsequently confirmed by numerical experiments. Verification of the model is performed by comparison with analytical solutions derived for counterflow conditions. Finally the model is applied to a particle dispersion experiment carried out recently in the Massachusetts Bay and comparisons with field data are presented.