Wind Drift in a Homogeneous Equilibrium Sea

This is the authors' abstract. We don't add key points for this paper.

A simple dynamical model is proposed for the near-surface drift current in a homogeneous, equilibrium sea. The momentum balance is formulated for a mass-weighted mean in curvilinear surface-conforming coordinates. Stokes drifts computed analytically for small wave slopes by this approach for inviscid linear sinusoidal and Pollard–Gerstner waves agree with the corresponding Lagrangian means, consistent with a mean momentum balance that determines mean parcel motion. A wave-modified mixing length model is proposed, with a depth-dependent eddy viscosity that depends on an effective ocean surface roughness length z 0 o , distinct from the atmospheric bulk-flux roughness length z 0 a , and an additional wave-correction factor ϕ w . Kinematic Stokes drift profiles are computed for two sets of quasi-equilibrium sea states and are interpreted as mean wind drift profiles to provide calibration references for the model. A third calibration reference, for surface drift only, is provided by the traditional 3%-of-wind rule. For 10-m neutral wind U 10 N ≤ 20 m s −1 , the empirical z 0 o ranges from 10 −4 to 10 m, while ϕ w ranges from 1.0 to 0.1. The model profiles show a shallow log-layer structure at the smaller wind speeds and a nearly uniform near-surface shear at the larger wind speeds. Surface velocities are oriented 10°–20° from downwind for U 10 N ≤ 10 m s −1 and 20°–35° from downwind for 10 ≤ U 10 N ≤ 20 m s −1 . A small correction to the drag coefficient is implied. The model predictions show a basic consistency with several sets of previously published near-surface current measurements, but the comparison is not definitive.