The aerodynamic drag of a free water surface

Abstract

The drag exerted by wind on a water surface has been measured in a tunnel 7·5 cm. wide and 7 m. long in which winds up to 14 m. /sec. can be made. The waves thus formed are similar to those seen at sea. A device increases the effective fetch and therefore the size of the waves. The drag is measured by the slope of the mean water surface. The shear-stress coefficient γ 2 a = τ / ρu 2 a increases nearly linearly with wind speed, and the drag therefore increases nearly with the cube of the speed. There is a not unsatisfactory agreement with field results of shear coefficient, when the wind velocity is extrapolated to the greater height at which it is usually measured over the sea. It is thought that this agreement between the drag of small laboratory waves and large field waves may show that the mechanism for drag is not controlled by the wave size or speed, but perhaps by the tiny wind ripples. The variation of wind speed with height has been measured. The profiles sometimes show anomalies in the zone up to about 8 cm. above the crests, there being slow layers of air between faster ones. The height of the anomalous zone increases as the waves become higher. Above 8 cm. the usual rough boundary law holds good. An empirical law is given for the shear stress as a function of the speed of the surface layer of water.