  We adapt the formalism of the statistical theory of 2D turbulence in the case
where the Casimir constraints are replaced by the specification of a prior
vorticity distribution. A new relaxation equation is obtained for the evolution
of the coarse-grained vorticity. It can be used as a thermodynamical
parametrization of forced 2D turbulence (determined by the prior), or as a
numerical algorithm to construct arbitrary nonlinearly dynamically stable
stationary solutions of the 2D Euler equation.
