  If a fluid flow is driven by a weak Gaussian random force, the nonlinearity
in the Navier-Stokes equations is negligibly small and the resulting velocity
field obeys Gaussian statistics. Nonlinear effects become important as the
driving becomes stronger and a transition occurs to turbulence with anomalous
scaling of velocity increments and derivatives. This process has been described
by V. Yakhot and D. A. Donzis, Phys. Rev. Lett. 119, 044501 (2017) for
homogeneous and isotropic turbulence (HIT). In more realistic flows driven by
complex physical phenomena, such as instabilities and nonlocal forces, the
initial state itself, and the transition to turbulence from that initial state,
are much more complex. In this paper, we discuss the Reynolds-number-dependence
of moments of the kinetic energy dissipation rate of orders 2 and 3 obtained in
the bulk of thermal convection in the Rayleigh-B\'{e}nard system. The data are
obtained from three-dimensional spectral element direct numerical simulations
in a cell with square cross section and aspect ratio 25 by A. Pandey et al.,
Nat. Commun. 9, 2118 (2018). Different Reynolds numbers $1 \lesssim {\rm
Re}_{\ell} \lesssim 1000$ which are based on the thickness of the bulk region
$\ell$ and the corresponding root-mean-square velocity are obtained by varying
the Prandtl number Pr from 0.005 to 100 at a fixed Rayleigh number ${\rm
Ra}=10^5$. A few specific features of the data agree with the theory but the
normalized moments of the kinetic energy dissipation rate, ${\cal E}_n$, show a
non-monotonic dependence for small Reynolds numbers before obeying the
algebraic scaling prediction for the turbulent state. Implications and reasons
for this behavior are discussed.
