  The planar Navier-Stokes equation exhibits, in absence of external forces, a
trivial asymptotics in time. Nevertheless the appearence of coherent structures
suggests non-trivial intermediate asymptotics which should be explained in
terms of the equation itself. Motivated by the separation of the different time
scales observed in the dynamics of the Navier-Stokes equation, we study the
well-posedness and asymptotic behaviour of a constrained equation which
neglects the variation of the energy and moment of inertia.
