Finite difference models for mass transport in partially stratified estuaries.
The development of computer models for mass transport in estuaries had been an important engineering activity for the past decade. However, only a limited amount of work has been done in modelling the two-dimensional characteristics of partially stratified estuaries. The goals of this study were (1) to develop computer models which could calculate time-varying vertical and horizontal mass transport in partially stratified estuaries; (2) to compare the accuracy and usefulness of explicit finite difference models and Crank-Nicolson implicit finite difference models; (3) to demonstrate the applicability of finite difference models to the mass transport characteristics of the Houston Ship Channel; and (4) to summarize existing information on one and two-dimensional mathematical models that have been applied to significant estuary problems.; Explicit and Crank-Nicolson finite difference models were developed for the one- and two-dimensional estuary equations with varying coefficients. The models were constructed to allow for the varying of parameters at any time at any grid point and were programmed in FORTRAN-IV computer language. Good accuracy was obtained by both types of models when proper time and distance increments were used. The Crank-Nicolson approach was found to be more accurate for a wider range of these increments. The concentration profiles for instantaneous releases and for steadystate conditions were analyzed. Accuracy was determined by comparison with analytical closed-form solutions. Models also were developed to analyze the profiles for biochemical oxygen demand and dissolved oxygen under time-changing conditions. these models can analyze both aerobic and anaerobic conditions and included provisions for analyzing the effects of mechanical reaeration. Applicability of these models to partially stratified estuaries was established by comparisons with dye study data from the houston ship channel. Extensions of the finite difference modeling techniques to other applications were discussed. In addition, future studies to determine the proper values for parameters such as dispersion, velocity, reaeration, and decay for a variety of conditions in partially stratified estuaries were outlined and recommended.