Spectra of thermally stratified turbulent flow with no shear

In this paper a new analytical approximation, concerning the integral ??k?WT(p) dp in the spectral equations (3), (4) is suggested. It is based on the physical idea about natural realization of the degree of interaction between the mean and fluctuating fields and is analytically expressed by the formulae (10, (12) and (13). In the extreme cases of strong and weak interaction the general expression (13) has (11) as its asymptotes.

The system of spectral equations (14), (15) is solved numerically and the result is presented in the figure. It is seen that in case of stable stratification, a general inertial range exists, in the middle of which a buoyancy subrange appears with slopes of the spectral curves as shown in the figure. The results eliminate the so far unresolved contradiction between the theories of Bolgiano and Lumley. Shur and agree well with the experimental data.