Empirical Parameterization of the Wind-induced Drift Currents

Results of measurements of the drift currents induced by waves and wind at the wavy water surface are presented. The measurements were executed by means of surface floats in a large tank with the dimensions of 32.5x1x2 m³. Three cases were studied: (i) regular (narrow-band) mechanical waves; (ii) irregular (wide-band) mechanical waves; and (iii) wind waves.

The measured surface-drift currents induced by mechanical waves, U_d, are compared with the Stokes drift at the surface, U_St, estimated by the well-known formula with the integral over a wave spectrum. In this case, it was found that ratio U_d / U_St is varying in the range 0.5 – 0.93 and slightly growing with the decrease of wave steepness, having no visible dependence on the breaking intensity. These estimations are used to separate the wind-induced drift current, U_dw, from the total drift at the presence of wind.

In the case of wind waves, the wind-induced part of the surface drift, U_dw, is compared with the friction velocity, u_*. In our measurements, the ratio U_dw / u_* varies systematically in the range 0.65 – 1.2. Taking into account the percentage of wave breaking, Br, the wave age, A, and the wave steepness, Ϭ = ak_p, it was found the parameterization:  U_dw = (Br + Ϭ A) u_*, which corresponds to the observations with the mean error less than 10%. For the first time, this ratio provides the dependence of the surface wind drift on the surface wave parameters.