On the Active Role of Temperature in Surface-Layer Turbulence

Abstract

Orthonormal wavelet expansions were derived and applied to atmospheric surface-layer turbulence measurements of temperature and vapor concentration under unstable and stable atmospheric stability conditions. These expansions were used to investigate both the statistical and spectral structure of turbulence simultaneously in space and scale using two tracers: temperature and specific humidity. It was found that at small wavenumbers, both temperature and specific humidity Fourier and wavelet spectra exhibit a ?1 power law behavior consistent with other atmospheric boundary-layer experiments. The mean values of the energy spectrum obtained from the wavelet analysis are in agreement with the classical Fourier counterparts. The wavelet flatness factors (values up to 10) indicate strong deviation from Gaussian statistics in space for the temperature fluctuations as the wavenumber increases. In contrast, the spatial wavelet flatness factor for the specific humidity exhibits near Gaussian statistics (values up to 4) for all wavenumbers. The wavelet skewness in space indicates that the specific humidity attains a near-isotropic state with increasing wavenumber for both stability conditions. Unlike the specific humidity, the temperature wavelet skewness in space did not decay with increasing wavenumber, indicating the presence of large eddy anisotropy in space. Land surface heating/cooling inhomogeneity appears to affect the local structure of turbulence, and therefore, at small scales temperature behaves as an active scalar when compared to specific humidity. The active role of temperature was also analyzed within the framework of Bolgiano's spectral theory. Deviations from Bolgiano's theory for the temperature spectrum were observed at all wavenumbers with measured energy power law behavior of |1.2|, which is less than the theoretical value of |7/5|. Conditional wavelet analysis was developed and used to investigate the nature of these deviations from Bolgiano's scaling law for the temperature measurements. It was found that by suppressing energy-containing and intermittent events, Bolgiano's scaling law for the temperature spectrum held under stable stability conditions. The effect of different wavelet basis functions on the statistical and spectral description of atmospheric turbulence was also considered.