Wind stress on a water surface

TLDR: In this paper, the vertical distribution of horizontal mean wind in the lowest 8 metres over a reservoir (1·6 km × 1 km) has been measured using sensitive anemometers freely exposed from a fixed mast in water 16 m deep, the fetch being more than 1 km.

Abstract: The vertical distribution of horizontal mean wind in the lowest 8 metres over a reservoir (1·6 km × 1 km) has been measured using sensitive anemometers freely exposed from a fixed mast in water 16 m deep, the fetch being more than 1 km. The resulting profiles are closely logarithmic, the small differences being systematic and possibly due to the thermal instability which existed when the measurements were made. The usual law for wind profiles in neutral stability is where u is the wind speed at height z, k is von Karman's constant, log z (0) the intercept on the log z axis, and u* the so-called friction velocity defined by τ0 = pu, τ0 being the surface drag and rH the density of the air. To characterize the profiles u*/k, their slope, was plotted in relation to z (0), their intercept; this allowed a direct comparison with other profiles, in particular those recently measured in a laboratory channel by Sibul. The agreement was better than expected and indicated that z (0) was comparatively independent of fetch and stability but was largely determined by u*. The relation between u* and z (0) agreed roughly with the simplest non-dimensional relation between them, gz (0)/u = constant, so that one is led to a generalized wind profile for flow over a water surface which specifies the drag, given the wind at one known height. An approximate value of the constant is 12·5. This expression can be compared with earlier work. The better wind-profile observations show rough agreement; the experimental scatter is necessarily large since a water surface is aerodynamically much smoother than most land surfaces, precision anemometry in difficult circumstances being required to provide sufficiently precise values. Oceanographic measurements of the tilt of water surfaces are in fair agreement at high wind speeds but at low wind speeds the data are conflicting. The early results which imply that the drag-coefficient (u/u2) increases with decreasing wind speed in light winds are thought to be in error; some support for this belief comes from recent estimates of drag using a modified ageostrophic technique, which agree roughly among themselves and with the general expression.