EULER-POINCARE MODELS OF IDEAL FLUIDS WITH NONLINEAR DISPERSION

We propose a new class of models for the mean motion of ideal incompre ssible fluids in three dimensions, including stratification and rotati on. In these models, the amplitude of the rapid fluctuations introduce s a length scale, alpha, below which wave activity is filtered by both linear and nonlinear dispersion. This filtering enhances the stabilit y and regularity of the new fluid models without compromising either t heir large scale behavior, or their conservation laws. These models al so describe geodesic motion on the volume-preserving diffeomorphism gr oup for a metric containing the H-1 norm of the fluid velocity.