  The macroscopic study of hydrodynamic turbulence is equivalent, at an
abstract level, to the microscopic study of a heat flow for a suitable
mechanical system. Turbulent fluctuations (intermittency) then correspond to
thermal fluctuations, and this allows to estimate the exponents tau_p and
zeta_p associated with moments of dissipation fluctuations and velocity
fluctuations. This approach, initiated in an earlier note, is pursued here more
carefully. In particular we derive probability distributions at finite Reynolds
number for the dissipation and velocity fluctuations, and the latter permit an
interpretation of numerical experiments. Specifically, if p(z)dz is the
probability distribution of the radial velocity gradient we can explain why,
when the Reynolds number increases, log p(z) passes from a concave to a linear
then to a convex profile for large z as observed. We show that the central
limit theorem applies to the dissipation and velocity distribution functions,
so that a logical relation with the lognormal theory of Kolmogorov and Obukhov
is established. We find however that the lognormal behavior of the distribution
functions fails at large value of the argument, so that a lognormal theory
cannot correctly predict the exponents tau_p and zeta_p.
