Wind Drift in a Homogeneous Equilibrium Sea

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 Z0_o, distinct from the atmospheric bulk-flux roughness length Z0_a, and 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_10N ≤ 20 m s⁻¹, the empirical Z0_o ranges from 10⁻⁴ m 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_10N ≤ 10 m s⁻¹ and 20°-35° from downwind for 10 ≤ U_10N ≤ 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. 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 Z0_o, distinct from the atmospheric bulk-flux roughness length Z0_a, and 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_10N ≤ 20 m s⁻¹, the empirical Z0_o ranges from 10⁻⁴ m 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_10N ≤ 10 m s⁻¹ and 20°-35° from downwind for 10 ≤ U_10N ≤ 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.