  A principle of maximum entropy is proposed in the context of viscous
incompressible flow in Eulerian coordinates. The relative entropy functional,
defined over the space of $L^2$ divergence-free velocity fields, is maximized
relative to alternate measures supported over the energy--enstrophy surface.
Since thermodynamic equilibrium distributions are characterized by maximum
entropy, connections are drawn with stationary statistical solutions of the
incompressible Navier-Stokes equations. Special emphasis is on the
correspondence with the final statistics described by Kolmogorov's theory of
fully developed turbulence.
