A two-dimensional hydrodynamic model of a tidal estuary

Abstract

A finite element model is described which is used in the computation of tidal currents in an estuary. This numerical model is patterned after an existing algorithm and has been carefully tested in rectangular and curve-sided channels with constant and variable depth. One of the common uncertainties in this class of two-dimensional hydrodynamic models is the treatment of the lateral boundary conditions. Special attention is paid specifically to addressing this problem. To maintain continuity within the domain of interest, ‘smooth’ curve-sided elements must be used at all shoreline boundaries. The present model uses triangular, isoparametric elements with quadratic basis functions for the two velocity components and a linear basis function for water surface elevation. An implicit time integration is used and the model is unconditionally stable. The resultant governing equations are nonlinear owing to the advective and the bottom friction terms and are solved iteratively at each time step by the Newton-Raphson method. Model test runs have been made in the southern portion of San Francisco Bay, California (South Bay) as well as in the Bay west of Carquinez Strait. Owing to the complex bathymetry, the hydrodynamic characteristics of the Bay system are dictated by the generally shallow basins which contain deep, relict river channels. Great care must be exercised to ensure that the conservation equations remain locally as well as globally accurate. Simulations have been made over several representative tidal cycles using this finite element model, and the results compare favourably with existing data. In particular, the standing wave in South Bay and the progressive wave in the northern reach are well represented.