Two-dimensional boundary-fitted circulation model in spherical coordinates

A two-dimensional, vertically averaged, unsteady circulation model, using a nonorthogonal boundary-fitted technique, was developed in spherical coordinates for predicting sea level and currents in estuarine and shelf waters. Both the dependent and independent variables are transformed into a curvilinear coordinate system. The governing equations are solved by a semiimplicit method in which the elevations are solved implicitly and the vertically averaged velocities are solved explicitly. The model employs a space-staggered grid system and a three-level time discretization. Truncation errors are second order both in space and time. The model was tested against analytic solutions for a standing wave in a closed basin, tidal circulation in a simple rectangular channel with an irregular grid system and various degrees of rotation, and tidal how in an annular section channel with quadratic bottom topography. The model was also tested against steady-state wind-induced setup in a closed irregular basin with constant depth represented by an irregular grid system. Comparison of the model predictions with the corresponding analytical solutions were very good. The model was applied to simulate tidal circulation in the Providence River. The agreement with available observations is very good. The model predicts that the tide exhibits a cooscillating wave pattern with tidal currents leading tidal elevation by 2.8 to 3.8 h depending on location for the M(2) tidal constituent. The M(4) and M(6) tidal components are significantly amplified because their frequency is close to the resonant frequency of the bay.