The Critical Richardson Number and Limit of Applicability of Monin-Obukhov Similarity Theory in the Stable Atmospheric Boundary Layer

Measurements of atmospheric small-scale turbulence made at five levels on a 20-m tower during the Surface Heat Budget of the Arctic Ocean experiment (SHEBA) are used to determine upper limit of applicability of the local similarity theory in the stable boundary layer (SBL). In this study, we derive the applicability limit based on spectral analysis of wind velocity and temperature fluctuations. It is found that the -5/3 Kolmogorov power-law in the inertial subrange for stable conditions is obeyed over a wide range of the stability parameters; but when both gradient Richardson number, Ri, and flux Richardson number, Rf, exceed a 'critical value' about 0.20-0.25, the inertial subrange associated with the Richardson-Kolmogorov cascade dies out and vertical turbulent fluxes become small. Some small-scale turbulence survives even in the supercritical regime, but this is non-Kolmogorov turbulence and it decays rapidly with further increasing stability. Our approach is based on the idea that the region of applicability of similarity theory for the flux-profile relationships and for any other properly scaled statistics of the turbulence in the SBL is the same as for the Kolmogorov turbulence. Monin-Obukhov similarity theory is based on the turbulent fluxes in the high-frequency part of the spectra that are associated with energy-containing/flux-carrying eddies. Spectral densities in this high-frequency band diminish as the Kolmogorov energy cascade weakens; therefore, applicability of local Monin-Obukhov similarity theory in the stable conditions is limited by inequalities Ri < Ri_cr and Rf < Rf_cr. However, it is found that Rf_cr = 0.20-0.25 is a primary threshold for applicability. Applying this prerequisite shows that the data follow classical Monin-Obukhov local z-less predictions after the irrelevant cases (non-Kolmogorov turbulence) have been filtered and thus removes the controversy associated with the z-less concept (http://arxiv.org/abs/1202.5066).