Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reynolds number of transition and large-scale properties of strong
  turbulence   A turbulent flow is characterized by velocity fluctuations excited in an
extremely broad interval of wave numbers $k> \Lambda_{f}$ where $\Lambda_{f}$
is a relatively small set of the wave-vectors where energy is pumped into fluid
by external forces. Iterative averaging over small-scale velocity fluctuations
from the interval $\Lambda_{f}< k\leq \Lambda_{0}$, where
$\eta=2\pi/\Lambda_{0}$ is the dissipation scale, leads to an infinite number
of "relevant" scale-dependent coupling constants ( Reynolds numbers )
$Re_{n}(k)=O(1)$. It is shown that in the i.r. limit $k\rightarrow
\Lambda_{f}$, the Reynolds numbers $Re(k)\rightarrow Re_{tr}$ where $Re_{tr}$
is the recently numerically and experimentally discovered universal Reynolds
number of "smooth" transition from Gaussian to anomalous statistics of spatial
velocity derivatives. The calculated relation $Re(\Lambda_{f})=Re_{tr}$
"selects" the lowest - order non-linearity as the only relevant one. This means
that in the infra-red limit $k\rightarrow \Lambda_{f}$ all high-order
nonlinearities generated by the scale-elimination sum up to zero.

7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
2
The categories of this paper are: math
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys