Departure from Kolmogorovs -5/3 law
 

I have a time dependent turbulent velocity signal and have computed a power spectral density. What is the significance of the slope, in what appears to be the inertial subrange, not being equal to -5/3? In some regions of the flow the slope is -5/3 but in other regions it is not. In the regions where the slope is not -5/3 the turbulence intensity is considerably less (but not 0) than the regions where the slope is -5/3. I suspect in some of these regions the turbulence is still developing. Could another potential explanation be that because the local turbulence intensities are small, the local turbulence Reynolds number is smaller and therefore the separation between the large scales and the small scales is not sufficient for the inertial subrange to form?

Also in some of these regions the slope is larger and in some regions it is smaller than -5/3.

k^-5/3 is only a theoretical law derived from theory... it assumes homogeneity, isotropy... in general flows there is no reasons to have appearence of this slope...