Semi-phenomenological model for a wind-drift current

Abstract: Some data of the drift current, Ud, measured on a wavy surface of water in a laboratory and the field, are briefly described. Empirical formulas for Ud are given, and their incompleteness is noted, regarding to absence of the drift current dependence on surface-wave parameters. With the purpose of theoretical justification of empirical formulas, a semi-phenomenological model of the phenomenon is constructed. It is basing on the known theoretical and empirical data about the three-layer structure of the air-water interface: 1) the air boundary layer, 2) the wave-zone, and 3) the water upper layer. It is shown that a presence of linear drift-current profile in the wave-zone, U(z), makes it possible to obtain a general formula for the drift current on the wavy water surface, Ud. This model is based on the balance equation for the momentum-flux and current-gradient, taking place in the wave-zone. The proposed approach allows us to give an interpretation of the empirical results, and indicate the direction of their further detailed specification.