Development and application of a three-dimensional boundary-fitted circulation model in Providence River

Document Type

Conference Proceeding

Date of Original Version



A nonorthogonal, contravariant formulation, of a three dimensional boundary fitted circulation model was developed in spherical coordinates. The model employs a split mode solution technique in which the exterior (vertically averaged) equations are solved by a semi-implicit technique and the interior (vertical structure) by an explicit procedure, except that the vertical diffusion terms are solved implicitly. Temporally and spatially the eddy viscosity and diffusivity are determined from a turbulent energy equation. The effect of stratification is empirically accounted for through dependence of the vertical mixing scale on the local Richardson number. The computational method is economical, stable, and accurate. The model's ability to predict the point vertical structure of tidal flow is tested against analytic solutions employing constant and linearly depth-varying eddy viscosities with a noslip condition at the bottom. 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 further tested against analytic solutions for steady residual flow generated by density gradient, wind, and river flow. Agreement between analytic and model solutions are good to excellent. The model was applied to simulate tidal and wind driven flow in Providence River and compared with field observations.

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