3-DIMENSIONAL HYDRODYNAMICS ON FINITE-ELEMENTS .1. LINEARIZED HARMONIC MODEL

The linearized, three-dimensional hydrodynamic equations are solved numerically for periodic motions, subject to a linear slip condition at the bottom. The structure of the linearized equations allows an exact uncoupling of the horizontal and vertical computations, so that they may be achieved sequentially rather than simultaneously, and without iteration. The solution strategy involves simple horizontal C**0 finite elements for the description of free surface elevation. Vertical variations in velocity may be treated analytically for some special variations of viscosity with depth; more generally, the finite element method is employed with one-dimensional elements. Because of the uncoupling, the entire three-dimensional solution scales as a two-dimensional vertically-averaged problem. The limiting two-dimensional problem may be solved as a Helmholtz-type problem for elevation alone, using established techniques. Solutions for test problems are compared with known analytic solutions. Some simple gridding rules are established for the vertical discretization. Finally, a field application is shown involving the tidal response of the Lake Maracaibo (Venezuela) system.