Stokes Drift and Wind Drift in a Rotating Equilibrium Sea

Abstract Stokes drift in a surface gravity wave field may be defined as the kinematic, mean wave-correlated component of fluid motion or as the dynamic, forced response to a mean wave-correlated pressure gradient. For linear, sinusoidal, nonrotating waves, the kinematic wave drift can be computed using Lagrangian, fixed- z Eulerian, or surface-conforming Eulerian means, where z is depth relative to the mean sea surface. The dynamic wave drift in a rotating, equilibrium wind sea depends on the forced-damped momentum balance for the drift. The forcing is taken as the wave-correlated pressure force on the free surface, which imparts momentum but no vorticity to the wave field. The damping presumably derives primarily from wave breaking, for which a mean rate of momentum loss is introduced through a damping time scale inferred from equilibrium wind-wave theory. The resulting forced-damped wave and mean wave-drift momentum balances are examined for both Eulerian means. It is concluded that in a rotating equilibrium sea with the Coriolis parameter computed at 40°N, the mean dynamic Stokes drift will be directed up to 10°–45° to the right of downwind, depending on depth, wavelength, and wind-wave amplitude or wind speed. The parameterized wave-breaking force and the wave drift for a rotating equilibrium sea spectral wave field are combined with a recently proposed, semiempirical, rotating equilibrium sea wind-drift model to obtain predictions of the combined wind and dynamic wave drift. This combined drift differs modestly but systematically from wind-drift-only predictions from the wind-drift model. The approach suggests a modified, dynamic-drift form of wave-averaged equations for wave–turbulence interactions.