Scaling of turbulence spectra measured in strong shear flow near the Earth’s surface

Within the lowest kilometer of the Earth's atmosphere, in the so-called atmospheric boundary layer, winds are often gusty and turbulent. Nearest to the ground, the turbulence is predominately generated by mechanical wall-bounded wind shear, whereas at higher altitudes turbulent mixing of heat and moisture also play a role.

The variance (square of the standard deviation) of the fluctuation around the mean wind speed is a measure of the kinetic energy content of the turbulence. This kinetic energy can be resolved into the spectral distributions, or spectra, as functions of eddy size, wavenumber, or frequency. Spectra are derived from Fourier transforms of wind records as functions of space or time corresponding to wavenumber and frequency spectra, respectively.

Atmospheric spectra often exhibit different subranges that can be distinguished and scaled by the physical parameters responsible for: (1) their generation; (2) the cascade of energy across the spectrum from large- to small-scale; and (3) the eventual decay of turbulence into heat owing to viscosity effects on the Kolmogorov microscale, in which the eddy size is only a fraction of a millimeter.

This paper addresses atmospheric turbulence spectra in the lowest part of the atmospheric boundary layer—the so-called surface layer—where the wind shear is strong owing to the nonslip condition at the ground. Theoretical results dating back to Tchen's early work in 1953 'on the spectrum of energy in turbulent shear flow' led Tchen to predict a shear production subrange with a distinct inverse-linear power law for turbulence in a strongly sheared high-Reynolds number wall-bounded flow, as is encountered in the lowest sheared part of the atmospheric boundary layer, also known as the eddy surface layer.

This paper presents observations of spectra measured in a meteorological mast at Høvsøre, Denmark, that support Tchen's prediction of a shear production subrange following a distinct power law of degree −1 in the lowest part of the atmospheric surface layer with the form $\sim {u}_{* }^{2}{k}^{-1},$ where ${u}_{* }$ is the surface friction velocity and $k$ is the wavenumber.

Tchen's turbulence theory is shown to be able to predict the measured spectra of the wind velocity component parallel to the mean wind direction for eddy sizes larger than the measurement height above the ground. An amended analytical model for the near-neutral surface layer spectrum is then proposed.

This model, which is applicable to the scaling of the $u$ spectrum at all heights in the surface layer, is obtained by a combination of Kaimal's classical spectral model for scaling the inertial subrange with Tchen's 1953 and 1954 proposed shear production subrange theory. The shear production-amended spectral model is compared with observations of ensemble-averaged near-neutral spectra selected during a nine-month measurement period from recordings from six sonic anemometers at heights of 10, 20, 40, 60, 80, and 100 m in the meteorological tower at the test site for large wind turbines in Høvsøre, Denmark.

Finally, potential applications of the new spectral model are discussed, in particular for use within the lowest one-third of the surface layer in which the production subrange component of the spectrum is most prominent. The new spectral model can supply wavenumber-resolved turbulent kinetic energies for the prediction of wind loads on buildings, bridges, and wind turbines, and its spectral parameterization can also be used for scale-dependent parameterization of, e.g., surface-released atmospheric dispersion calculations for regions close to the ground.