A Semi-phenomenological Model for Wind-Induced Drift Currents

Empirical relations for the wind-induced drift current, U-d, measured at a wavy water surface in a laboratory and in the field, are presented and discussed. A relatively large value of U-d with respect to the friction velocity in water is highlighted, and it is noted that the empirical relations are incomplete, as they do not describe the drift-current dependence on surface-wave parameters. With the purpose of theoretical justification of these empirical facts, a semi-phenomenological model for the wind-induced drift current is constructed. It is based on the known theoretical results and empirical data related to the three-layer structure of the wavy air-water interface, which includes: (i) the air boundary layer, (ii) the wave zone, and (iii) the water boundary layer. The linear profile of drift current U-d(z), found empirically in the wave zone, allows the general relation for U-d to be determined. It is based on the equation of balance between the wind-induced momentum flux, tau, and the vertical gradient of drift current dU(d)(z)/dz in the wave zone. The model provides interpretation of the empirical results and indicates a means for their further specification.