Scaling Properties of an Inviscid Mean-Motion Fluid Model

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.