A three-dimensional boundary fitted circulation model in spherical coordinates

Muslim Muin, University of Rhode Island


A spherical coordinate nonorthogonal, contravariant formulation, three-dimensional boundary-fitted circulation model has been developed, tested, and applied to the Providence River. The model employs a split mode technique in which the governing equations are divided into an exterior (vertically averaged) and interior modes (vertical structure).^ The first manuscript is focused on the development, testing, and application of the vertically averaged form of the circulation model. The model was tested against analytic solutions for tidal forcing in an annular section channel, simple channel with an irregular grid system, and an arbitrarily rotated channel. The model was also tested against steady state wind-induced setup in a closed irregular basin with constant depth. The model was then applied to simulate multiconstituent tidal flow in Upper Narragansett Bay and compared to available tidal current and height data. The agreement between the model predictions and observations is excellent.^ The second manuscript extends the vertically averaged model to include vertical velocity structure. The capability of the model to simulate three dimensional tidal flow was tested against an exact solution for an annular section channel with quadratically varying bathymetry. The model was also tested for steady residual flow generated by wind, river, and density forcing. The vertical eddy viscosity and diffusivity were determined from a one equation turbulent energy model.^ The third manuscript describes the application of the three dimensional model to Upper Narragansett Bay and the Providence River. The model, with turbulence sub-model, is successfully applied to simulate the tidal surface elevations and currents in the area. The agreement between the model predicted and observed currents for the principal seven tidal constituents is very good. The model was also applied to simulate the residual flow under constant wind forcing from a variety of directions. The results show the importance of the dredged channel in controlling the flows. For along river axis winds the wind induced currents flow against the wind direction in the dredged channel while those in shallow water on either side are in the direction of the wind. ^

Subject Area

Physical Oceanography|Engineering, Civil|Engineering, Mechanical

Recommended Citation

Muslim Muin, "A three-dimensional boundary fitted circulation model in spherical coordinates" (1993). Dissertations and Master's Theses (Campus Access). Paper AAI9421909.