Wave-modified Ekman current solutions for the vertical eddy viscosity formulated by K-Profile Parameterization scheme

A Fourier series solution is presented for the time-dependent wave-modified Ekman current resulting from the Stokes drift, wind input and wave dissipation for the vertical eddy viscosity formulated by the K-Profile Parameterization scheme. An exact steady solution can be concluded as a special example. The parameters involved in the solution can be determined by the two-dimensional surface wave spectrum, wind vector, the Coriolis parameter and the densities of air and water. As illustrative examples, for a fully developed wind-generated sea with different wind speeds, wave-modified current profiles are calculated and compared with those when wave is absent or includes only the effect of the Stokes drift by using the extended Donelan and Pierson (1987) spectrum, the WAM wave model formulation for wind input energy to waves, and wave energy dissipation converted to currents. The exact solutions are also compared with well-known published observational data of the Ekman layer. It is shown that the solution presented is a reasonable analytic current model with the right dependence on wind, wave and Coriolis parameter for unstratified Ekman layer.