The simulation of estuarine circulations with a fully three-dimensional numerical model

The Navier-Stokes, salinity and continuity equations in the Boussinesq approximation are spatially integrated on the elementary computational cells to provide equations for the temporal rate of change of the fluxes through every cell's face and of the mean salinity in every cell. The effect of the spatial subgrid scales is lumped together with the Reynolds stresses generated by the temporal discretization procedure, and modeled by a simple Fickian relationship. The pressure field in the momentum equations is split up into a hydrostatic and a dynamic parts, the latter obtained as the solution to a finite differencesPoisson equation. The three momentum equations and the salinity equation are independently updated by a forward stepping scheme. The free surface is updated by a mass conserving scheme. Required boundary conditions are river inflows and surface elevation at the sea as a function of time, as well as applied winds and atmospheric pressure. The model has been implemented in a Fortran code. It admits arbitrary coastal boundaries, openings to the sea, river inflows and bathymetry, imposed by the user through data cards. Idealized test cases are used to show that the model behaves as physically expected. A coarse application to Chesapeake Bay shows qualitatively correct results and the need to incorporate a less naive representation for the sub-grid scales.