SOLUTION OF THE 3D LINEAR HYDRODYNAMIC EQUATIONS USING AN ENHANCED EIGENFUNCTION APPROACH

A method is presented for solving the 3D hydrodynamic equations in homogeneous sea regions using the Galerkin approach in the vertical with a mixed basis set. The basis set is composed of eigenfunctions of the eddy viscosity profile and a fixed function through the vertical, the amplitude of which is related to the externally applied surface wind stress. By this means the high-shear near-surface, which has previously been difficult to resolve using eigenfunction expansions, is accurately represented in the solution. The computational advantages of this approach compared with other basis functions, in terms of computer time and memory, and the ease of implementation on parallel processors with vector facilities are briefly discussed. The accuracy of the method and the choice of the additional function is demonstrated for the problem of wind-induced currents in a rectangular sea region. Calculations clearly show that for wind-induced currents this new approach is significantly more accurate than the 'classical' eigenfunction method. Also, the new method retains the advantages of the eigenfunction approach, namely insight into the mechanisms involved and ease of implementation on vector-parallel computers, together with minimization of computer time and memory.