The conceptual framework for modelling the inertial subrange is strongly influenced by the Kolmogorov cascade phenomena, which is now the subject of significant reinterpretation. It has been argued that the effects of boundary conditions influence large-scale motion and direct interaction between large and small scales is possible by means other than passing sequentially through the full cascade. Using longitudinal (u) and vertical (w) velocity and temperature (T) time series measurements, collected in the atmospheric surface layer ( ASL), we evaluate whether the inertial subrange is influenced by different stability regimes.
For each measurement run in each stability class and for each of the three scalars--we calculate the quasi-Hurst exponents (H) and test their equality by an ANOVA procedure. We also find intrinsic distributional properties of the wavelet coefficients (Mallat's model) and investigate the behavior of scale and shape parameters in each of the stability classes. We propose a model with statistics adjusted by stability considerations and contrast the results with empirical findings.
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