Intermittency of Atmospheric Turbulence

Abstract

Dimensionless structure functions such as kurtosis of the velocity gradients are computed from aircraft data for a variety of atmospheric situations in order to characterize the intermittency of the turbulence. It is necessary to distinguish between small scale intermittency of the velocity gradients organized by the individual main eddies and global intermittency associated with patchiness of turbulence on scales larger than the main eddies. Failure to make such a distinction can lead to ambiguity and inability to recognize contamination of statistics by sampling problems. The sharp edges of the main eddies contribute to the small scale intermittency as measured by the kurtosis of the velocity gradients and other intermittency statistics. However, for some of the strongly stratified cases, global intermittency increases the kurtosis by a factor of 2 or 3 in which case the statistics reflect the global spatial variability of the turbulence (patchiness) more than the local characteristics of the turbulence itself. As a result, the kurtosis increases with record length as more of the larger scale spatial variability is incorporated. in such case record partitioning is employed to construct more useful estimates of the small scale intermittency. The variation of the structure kurtosis with separation distance is normally found to obey the Kolmogorov similarity theory which has been modified to include the influence of small scale intermittency. However, the modified theory does not describe decaying turbulence nor turbulence with strong global intermittency. The dimensionless structure function for artificial turbulence and mixtures of distributions are studied analytically. The usual dimensional structure function responds to the scale of the main building blocks (simulated eddies) while the structure kurtosis and other dimensionless moments respond to the spatial scale of the edges of the building blocks where gradients are particularly large and contribute to the tails of the frequency distribution. The dimensionless structure function of the artificial turbulence is also augmented by global intermittency posed in terms of mixtures of frequency distributions. This analytical analysis appears to explain the observed enhancement of the dimensionless structure kurtosis by the sharp edges of the main eddies and by the global intermittency of those records with strong thermal stratification.