| Abstract: | A theory is outlined for time-dependent currents induced near the sea surface in deep water, away from coastal boundaries, by a variable wind stress and deep-water wave field. It is based on the theory of Weber (1983) which uses a second-order perturbation expansion of the Navier-Stokes equations in Lagrangian coordinates and includes the Coriolis effect. It uses an eddy viscosity formulation for both wave dissipation and momentum transfer within the current field: the eddy viscosity ν may be allowed to vary with depth. The wind stress may be time-varying and the wave field may vary in both space and time.For the case of a constant ν, the results agree with those of Ursell (1950), Hasselmann (1970) and Pollard (1970) in the limit ν→0, and the steady-state results agree with those of Weber. For a particular case of depth-varying ν, results (obtained from numerical simulations) are in better general agreement with observations of wind-induced surface drift than when a constant ν is used.An outline is given of the application of the theory to the case of a random sea state. There are good prospects for using output data from numerical wave prediction models to drive the equations of this near-surface current model. |
