Intermittency, local isotropy, and non-Gaussian statistics in atmospheric surface layer turbulence

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Abstract
Orthonormal wavelet expansions are applied to atmospheric surface layer velocity and temperature measurements above a uniform bare soil surface that exhibit a long inertial subrange energy spectrum. In order to investigate intermittency effects on Kolmogorov’s theory, a direct relation between the nth‐order structure function and the wavelet coefficients is derived. This relation is used to examine deviations from the classical Kolmogorov theory for velocity and temperature in the inertial subrange. The local nature of the orthonormal wavelet transform in physical space aided the identification of events directly contributing to intermittency buildup at inertial subrange scales. These events occur at edges of large eddies and contaminate the Kolmogorov inertial subrange scaling. By suppressing these events, the statistical structure of the inertial subrange for the velocity and temperature, as described by Kolmogorov’s theory, is recovered. The suppression of intermittency on the nth‐order structure function is carried out via a conditional wavelet sampling scheme. The conditioned wavelet statistics reproduced the Kolmogorov scaling (up to n=6) in the inertial subrange and result in a zero intermittency factor. The conditional wavelet statistics for the mixed velocity temperature structure functions are also presented. It was found that the conditional wavelet statistics for these mixed moments result in a thermal intermittency parameter consistent with other laboratory and field measurements. The relationship between Kolmogorov’s theory and near‐Gaussian statistics for velocity and temperature gradients is also considered.