Development and application of a three-dimensional orthogonal coordinate semi-implicit hydrodynamic model

A three-dimensional, orthogonal coordinate semi-implicit hydrodynamic model in spherical coordinates that can be applied to estuarine, coastal sea, and continental shelf waters is presented. A generalized orthogonal coordinate transformation on the horizontal and a sigma coordinate transformation on the vertical, are applied to the governing equations. The governing equations are decomposed into exterior and interior modes and solved using a semi-implicit solution technique. Second-order accurate spatial and temporal discretization schemes are used on a space staggered grid. A simple flooding and drying technique is used to model the tidal flats. The model results are tested against analytical solutions for tidal circulation in an annular channel and steady residual flow generated by wind, and density differences in a rectangular channel. The predictions from the model showed very good comparison with analytical solutions for all the test cases. Three-dimensional circulation in Narragansett Bay was then studied using the developed model. The model predicted surface elevations, three-dimensional instantaneous and mean currents, salinities, and temperatures in Narragansett Bay are compared with the observations. Mean errors in the model predicted surface elevations and velocities are less than 3% and 15%, respectively. The spring and neap cycles, the shorter duration but stronger ebb dominant currents and the double flood phenomena seen in the observations are reproduced by the model. The mean estuarine currents, and the sub-tidal currents seen in the observations are also well reproduced by the model. Correlation coefficients for salinity and temperatures exceed 0.95 and 0.87, respectively.