Based on recent advances in the theory of
Euler-Poincaré (EP) equations with advected
parameters and using the methods of Hamilton's
principle asymptotics and averaged Lagrangians,
we propose a new class of models for ideal
incompressible fluids in three dimensions,
including stratification and rotation for GFD
applications. In these models, the amplitude of
the rapid fluctuations introduces a length
scale,
, below which wave activity is
filtered by both linear and nonlinear
dispersion. This filtering enhances the
stability and regularity of the new fluid
models without compromising either their large
scale behavior, or their conservation laws.
These models also describe geodesic motion on
the volume-preserving diffeomorphism group for
a metric containing the
H1 norm of the fluid velocity.
