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.
