Wind Drift in a Homogeneous Equilibrium Sea

Abstract

Abstract 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 z0o, distinct from the atmospheric bulk-flux roughness length z0a, and an additional wave-correction factor ϕw. 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 U10N ≤ 20 m s−1, the empirical z0o ranges from 10−4 to 10 m, while ϕw 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 U10N ≤ 10 m s−1 and 20°–35° from downwind for 10 ≤ U10N ≤ 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.