  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 the spectral analysis of wind velocity and air temperature fluctuations, it
is shown that, when both of the gradient Richardson number, Ri, and the flux
Richardson number, Rf, exceed a 'critical value' of 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 this 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
Richardson-Kolmogorov energy cascade weakens; therefore, the applicability of
local Monin-Obukhov similarity theory in stable conditions is limited by the
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 (turbulence without the Richardson-Kolmogorov
cascade) have been filtered out.
