  Asymptotically large Reynolds number hydrodynamic turbulence is characterized
by multi-scaling of moments of velocity increments and spatial derivatives.
With decreasing Reynolds number toward $R_{\lambda}=R^{tr}_{\lambda}\approx
9.0$, the anomalous scaling disappears in favor of the "normal" one and
close-to-Gaussian probability densities [Yakhot \& Donzis, {\bf 119}, 044501
(2017)]. The nature of this transition and its universality are subjects of
this work.
  Here we consider Benard convection ( Prandtl number $Pr=1$) between infinite
horizontal plates. It is shown that in this system the "competition" between
Bolgiano and Kolmogorov processes, results in small-scale velocity fluctuations
driven by effective "large-scale" Gaussian random temperature field. Therefore,
the intermittent dynamics of velocity derivatives are similar or even identical
to that in homogeneous and isotropic turbulence generated by the large-scale
random forcing. It is shown that low-Rayleigh number instabilities make the
problem much more involved and may lead to transition from Gaussian to
exponential PDF of the temperature field. The developed {\it mean-field theory}
yielded dimensionless heat flux $Nu\propto Ra^{\beta}$ with $\beta\approx
15/56\approx 0.27$, close to the outcome of Chicago experiment. These results
point to an unusual small-scale universality of turbulent flows. It is also
shown that at $R_{\lambda}\leq 9.0$, a flow "remembers" its laminar background
and, therefore, cannot be universal.
