Analytical solutions for wind and wave induced ocean currents.

摘要

Analytical solutions are given for a simple one dimensional wind and wave driven ocean current model. The model is based on Jenkins' [10] theory which explicitly includes wind-generated waves and the impact of waves on currents is built into both the momentum equation and the ocean surface boundary condition. To simplify the discussion, we assume the eddy viscosity nu is a function of wind speed. Also, we use depth-averaged estimates for the Stokes drift, the momentum from wind to waves and the momentum from waves to current. Without waves, it is proven that the time dependent current converges to a steady current if the wind is constant, whereas when waves are present, the components of the current form a time-dependent circle. The center and radius of the circle are defined by the wave effects, including Stokes drift, the momentum transfer due to wave dissipation and the momentum transfer due to wind input. A wave model (Resio [18], Resio and Perrie [19]) is used to generate the two dimensional wave spectrum. In high winds, the impacts of the momentum transfer due to wave dissipation and the momentum transfer due to wind input on currents are shown to be as important as the effects due to Stokes drift. The analytical solutions are shown to be able to reliably represent the main physical currents in the upper ocean. These analytical solutions are important because they can be used as benchmarks in comparisons with numerical current models. They also can be potentially used in time-critical situations (e.g. oil spill, search and rescue emergencies) because they require very little computing time because of their simplicity.