On the determination of vertical structure functions for time-dependent flow problems

A method of solving the viscous three-dimensional hydrodynamic equations is developed using an expansion of vertical structure functions (modes). Both slip and no-slip bottom boundary conditions can be incorporated in the method. Vertical structure functions for arbitrary vertical variations of viscosity are computed using either the Runge-Kutta-Merson method or an expansion in terms of spline functions. The accuracy and relative merits of these two methods is compared and contrasted. The influence of vertical eddy viscosity upon modal structure, and profiles of wind drift currents is examined for both homogeneous and stratified sea regions. The excitation and subsequent decay of the modes in response to a suddenly applied wind stress is considered, as is the influence of depth and viscosity upon the rate of convergence of expansions of vertical structure functions.