Wave Dependence of Sea-Surface Wind Stress

Abstract

Distribution of the wind stress over the oceans is usually estimated by using a bulk formula. It contains the squared 10-m wind speed multiplied by the drag coefficient, which has been assumed in many cases to be a weak function of the 10-m wind speed. Over land the important role of thermal stratification has been clearly recognized, but over the sea the influence of wind waves is less well documented. This paper presents evidence showing the likelihood that the influence of the wind waves can also be large. Charnock proposed an expression for the marine atmospheric boundary layer roughness parameter, z0, which depended only on the wind friction velocity, u? and the acceleration of gravity, g. Toba and Koga have recently proposed an alternative expression for flow over growing wind waves, which are in local equilibrium with the wind, given by a form including the wind-wave spectral peak frequency explicity. The criterion for local equilibrium of the wave field with the wind is its consistency with the 3/2power law between nondimensional wave height and wave period normalized by u? and g. The differences between these expressions are significant. The two expressions are compared with a composite dataset which comprises some representative data from laboratories and tower stations together with data from storms at an oil producing platform in Bass Strait, Australia. In these storms strong winds up to 25 m s?1 and large wind waves up to 12 s in significant wave period, from a direction of long fetch, lasted for two or three days. The composite dataset shows that the drag coefficient CD depends also on the sea scale and that in storm conditions CD can be larger by a factor of two to three than the value that Charnock's expression usually predicts. Further experiments focussing on the examination of the effect of ocean waves on the wind stress are recommended.