Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reynolds number dependence of Lyapunov exponents of turbulence and fluid
  particles   The Navier-Stokes equations generate an infinite set of generalized Lyapunov
exponents defined by different ways of measuring the distance between
exponentially diverging perturbed and unperturbed solutions. This set is
demonstrated to be similar, yet different, from the generalized Lyapunov
exponent that provides moments of distance between two fluid particles below
the Kolmogorov scale. We derive rigorous upper bounds on dimensionless Lyapunov
exponent of the fluid particles that demonstrate the exponent's decay with
Reynolds number $Re$ in accord with previous studies. In contrast, terms of
cumulant series for exponents of the moments have power-law growth with $Re$.
We demonstrate as an application that the growth of small fluctuations of
magnetic field in ideal conducting turbulence is hyper-intermittent, being
exponential in both time and Reynolds number. We resolve the existing
contradiction between the theory, that predicts slow decrease of dimensionless
Lyapunov exponent of turbulence with $Re$, and observations exhibiting quite
fast growth. We demonstrate that it is highly plausible that a pointwise limit
for the growth of small perturbations of the Navier-Stokes equations exists.

29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th