Transient Ocean Currents Induced by Wind and Growing Waves

Abstract

Abstract A theoretical nonlinear model for wind- and wave-induced currents in a viscous, rotating ocean is developed. The analysis is based on a Lagrangian description of motion. The nonlinear drift problem is formulated such that the solution depends on a linearly increasing eddy viscosity in the water, the wave-growth rate, and the periodic normal (or tangential) wind stress at the sea surface. Particular calculations are performed for surface-stress distributions and growth rates obtained from asymptotic analysis of turbulent atmospheric flow, where the Reynolds stress is modeled by an eddy-viscosity assumption. For growing waves the wave-induced current develops in time. The calculations are terminated when the steepness of the fastest-growing waves reach that of a saturated sea. At this point, the magnitude of the wave-induced surface current is 8–9 times larger than the friction velocity in the water, and the direction of the current is deflected 2°–10° to the right of the wave-propagation direction.