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

TL;DR

This study analyzes high-resolution offshore wind speed data over 20 months, revealing turbulence signatures in power spectra and structure functions, and compares these findings with atmospheric turbulence at different altitudes.

Contribution

It provides a detailed analysis of wind turbulence signatures across scales and links offshore wind turbulence characteristics with atmospheric turbulence at various altitudes.

Findings

Energy spectra show turbulence-like scaling at high frequencies.

Third-order structure function indicates a transition point at a specific frequency.

The crossover length scale (~400 km) is consistent across different atmospheric altitudes.

Abstract

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 $f_{\rm\scriptscriptstyle 2D}$, a rapid rise of $fS(f)$ occurs. An analysis of the third-order structure function $D_3(\tau)$ of wind speed differences for a given time lag $\tau$ shows a rapid change from negative to positive values of $D_3(\tau)$ at $\tau\simeq 1/f_{\rm\scriptscriptstyle 2D}$. 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 $D_3$, and with the third power for positive $D_3$. 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.