  We investigate universality of the Eulerian velocity structure functions
using velocity fields obtained from the stereoscopic particle image velocimetry
(SPIV) technique in experiments and the direct numerical simulations (DNS) of
the Navier-Stokes equations. We show that the numerical and experimental
velocity structure functions up to order 9 follow a log-universality; we find
that they collapse on a universal curve, if we use units that include
logarithmic dependence on the Reynolds number. We then investigate the meaning
and consequences of such log-universality, and show that it is connected with
the properties of a "multifractal free energy", based on an analogy between
multifractal and themodynamics. We show that in such a framework, the existence
of a fluctuating dissipation scale is associated with a phase transition
describing the relaminarisation of rough velocity fields with different Holder
exponents. Such a phase transition has been already observed using the
Lagrangian velocity structure functions, but was so far believed to be out of
reach for the Eulerian data.
