FINITE ELEMENT MODEL OF TWO LAYER COASTAL CIRCULATION

John D. Wang, Jerome J. Connor

Abstract


A set of "averaged partial differential equations for the circulation in a two layered coastal water is established by assuming each layer to be vertically homogeneous and by performing a vertical integration over the layer thicknesses. Since the phenomena to be investigated typically consist of long waves such as a tidal wave, the hydrostatic pressure assumption is also introduced. The finite element method is employed to transform the partial differential equations to a discrete system of ordinary differential equations which are solved using an implicit time stepping method similar to the trapezoidal rule, but with the variables (elevation and flows) staggered in time. A linear stability analysis shows the initial value problem to be unconditionally stable. In practice, instability due to boundary conditions and non-linearity sets in. Comparisons between computed and analytical solutions for simple cases give good agreement. The tidal excitation of Massachusetts Bay, represented as a rectangular basin with opening on one side is presented as an illustrative example.

Keywords


finite element; circulation; two dimensional circulation

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