A Finite Element Simulation Model for the Study of Wind Driven and Tidal Current a Shallow Coastal Lagoon

Abstract

The equations required for modeling three dimensional hydrodynamics (space two dimension and time) in a shallow coastal lagoon are derived from the three dimensional Navier-Stokes equation and Continuity equation by integrating and taking the average along water depth. The wind stress at the surface, the friction stress at the bottom, the Coriolis parameter, eddy viscosity and shore line geometry are incorporated in the mathematical model. Both the analytical and numerical approaches cannot be used for solving the governing Navier-Stokes equations from the existence of the nonlinear convective terms and complexity of equations and geometry involved, the time dependent shallow water equations are solved using Galerkin’s method. A finite element formulation for solving the shallow water equations is presented for the prediction of wind-driven and tidal currents in a coastal lagoon.