Signatures of geostrophic turbulence in power spectra and third-order structure function of offshore wind speed fluctuations

We analyze offshore wind speeds with a time resolution of one second over a long period of 20 months for different heights above the sea level. Energy spectra extending over more than seven decades give a comprehensive picture of wind fluctuations, including intermittency effects at small length scales and synoptic weather phenomena at large scales. The spectra S(f) show a scaling behavior consistent with three-dimensional turbulence at high frequencies f, followed by a regime at lower frequencies, where fS(f) varies weakly. Lowering the frequency below a crossover frequency [Formula: see text] , a rapid rise of fS(f) occurs. An analysis of the third-order structure function [Formula: see text] of wind speed differences for a given time lag [Formula: see text] shows a rapid change from negative to positive values of [Formula: see text] at [Formula: see text] . Remarkably, after applying Taylor’s hypothesis locally, we find the third-order structure function to exhibit a behavior very similar to that obtained previously from aircraft measurements at much higher altitudes in the atmosphere. In particular, the third-order structure function grows linearly with the separation distance for negative [Formula: see text] , and with the third power for positive [Formula: see text] . This allows us to estimate energy and enstrophy dissipation rates for offshore wind. The crossover from negative to positive values occurs at about the same separation distance of 400 km as found from the aircraft measurements, suggesting that this length is independent of the altitude in the atmosphere.