The Alignment of the Mean Wind and Stress Vectors in the Unstable Surface Layer

A significant non-alignment between the mean horizontal wind vector and the stress vector was observed for turbulence measurements both above the water surface of a large lake, and over a land surface (soybean crop). Possible causes for this discrepancy such as flow distortion, averaging times and the procedure used for extracting the turbulent fluctuations (low-pass filtering and filter widths etc.), were dismissed after a detailed analysis. Minimum averaging times always less than 30 min were established by calculating ogives, and error bounds for the turbulent stresses were derived with three different approaches, based on integral time scales (first-crossing and lag-window estimates) and on a bootstrap technique. It was found that the mean absolute value of the angle between the mean wind and stress vectors is highly related to atmospheric stability, with the non-alignment increasing distinctively with increasing instability. Given a coordinate rotation that aligns the mean wind with the x direction, this behaviour can be explained by the growth of the relative error of the u–w component with instability. As a result, under more unstable conditions the u–w and the v–w components become of the same order of magnitude, and the local stress vector gives the impression of being non-aligned with the mean wind vector. The relative error of the v–w component is large enough to make it undistinguishable from zero throughout the range of stabilities. Therefore, the standard assumptions of Monin–Obukhov similarity theory hold: it is fair to assume that the v–w stress component is actually zero, and that the non-alignment is a purely statistical effect. An analysis of the dimensionless budgets of the u–w and the v–w components confirms this interpretation, with both shear and buoyant production of u–w decreasing with increasing instability. In the v–w budget, shear production is zero by definition, while buoyancy displays very low-intensity fluctuations around zero. As local free convection is approached, the turbulence becomes effectively axisymetrical, and a practical limit seems to exist beyond which it is not possible to measure the u-w component accurately.