Ekman Currents and Mixing due to Surface Gravity Waves

Jan Erik Weber Institute of Geophysics, University of Oslo, Blindern, Oslo 3, Norway

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Abstract

The steady Ekman boundary-layer current is studied theoretically for the case when the eddy viscosity is proportional to the shear of the wave orbital velocity in a turbulent wave, times the square of a mixing length (Kitaigorodsky, 1961). Assuming a fully developed sea, the wave characteristics, and hence the eddy viscosity distribution with depth, are determined by the wind. The momentum equation is solved numerically to yield the Ekman current as a function of the wind speed. The results show that the magnitude of the Ekman surface current lies between 2.1 and 3% of the wind speed at 10 m height. The deflection angle away from the wind direction is a monotonic decreasing function of wind speed. It varies from 36 to 25° for winds between 5 and 30 m s−1.

Abstract

The steady Ekman boundary-layer current is studied theoretically for the case when the eddy viscosity is proportional to the shear of the wave orbital velocity in a turbulent wave, times the square of a mixing length (Kitaigorodsky, 1961). Assuming a fully developed sea, the wave characteristics, and hence the eddy viscosity distribution with depth, are determined by the wind. The momentum equation is solved numerically to yield the Ekman current as a function of the wind speed. The results show that the magnitude of the Ekman surface current lies between 2.1 and 3% of the wind speed at 10 m height. The deflection angle away from the wind direction is a monotonic decreasing function of wind speed. It varies from 36 to 25° for winds between 5 and 30 m s−1.

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