Formulating Layered and Semi-Analytic Finite Element Flow Programs with Variable Eddy Viscosity

Abstract

A number of different finite element programs for the analysis of flows in lakes and oceans have evolved over the past several years under an increased demand to understand the hydrodynamics of these natural bodies of water. These programs are all founded on the basic Eulerian momentum and continuity equations for incompressible flow. Different analysis formulations have evolved depending on the importance of different flow velocities. Three dimensional transient flow programs are generally required to provide a reasonable description of the major flow characteristics. Although there are a number of ways to classify finite element programs of this type one feature which can be used to distinguish two groups is the means by which the vertical structure of the flow is represented. The two general possibilities are to use a semianalytic formulation for the vertical structure or use a Galerkin based finite element or spectral formulation. Semi-analytic numerical formulations incorporating finite elements (Cheng, 1977; Liggett,1973) have been successfully used in the analysis of circulations in lakes. Fully three dimensional Galerkin based finite element models are generally of the multi-layered type (Kawahara, 1980; Wang and Connor, 1975; King and Norton, 1973; Koutitas, 1980). Single layered finite element models have also been formulated using higher degree polynomial bases functions (Laible, 1980) or Fourier series (Koutitas, 1978) to model the vertical structure of the flow.