  An inviscid two-dimensional fluid model with nonlinear dispersion that arises
simultaneously in coarse-grained descriptions of the dynamics of the Euler
equation and in the description of non-Newtonian fluids of second grade is
considered. The scaling of the equilibrium states of this model for conserved
energy and enstrophy retains the corresponding scaling for the Euler equations
on the large scales and at the same time greatly deemphasizes the importance of
small scales. This is the first clear demonstration of the beneficial effect of
nonlinear dispersion in the model, and should highlight its utility as a
subgrid model in more realistic situations.
