The Critical Richardson Number and Limits of Applicability of Local Similarity Theory in the Stable Boundary Layer

Details The Critical Richardson Number and Limits of Applicability of Local Similarity Theory in the Stable Boundary Layer The Critical Richardson Number and Limits of Applicability of Local Similarity Theory in the Stable Boundary Layer

2012-02-23

arxiv.org/abs/1202.5066v1

Physics

Atmospheric and Oceanic Physics

Manuscript submitted to Boundary-Layer Meteorology (16 February 2012)

Scientific paper

Measurements of atmospheric turbulence made over the Arctic pack ice during the Surface Heat Budget of the Arctic Ocean experiment (SHEBA) are used to determine the limits of applicability of Monin-Obukhov similarity theory (in the local scaling formulation) in the stable atmospheric boundary layer. Based on spectral analysis of wind velocity and air temperature fluctuations, it is shown that 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 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. 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 out.

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