Statistics of the Wind-Speed Difference Between Points with Cross-Wind Separation

This note reports statistics of instantaneous wind-speed differences between pairs of points in the surface layer sharing equal height (z = 2-3 m), but separated by large distances (ranging up to 70 m) along an axis transverse to the direction of the mean wind. To provide context for the analysis, some elementary statistical properties of point-point signal differences are first derived, then, on the basis of observations from a transect of anemometers, correlations are provided that allow an estimate of the root-mean-square daytime speed difference. During unstable daytime conditions the prevalence of eddies of a scale larger than instrument separation ensured paired instruments sampled highly correlated winds, whereas at night paired instruments sampled weaker fluctuations (largely) independently. The probability density function of the wind-speed difference proved roughly invariant with respect to the micrometeorological state, and tends towards a Gaussian as separation becomes large.