  We examine long-time properties of the ideal dynamics of three--dimensional
flows, in the presence or not of an imposed solid-body rotation and with or
without helicity (velocity-vorticity correlation). In all cases the results
agree with the isotropic predictions stemming from statistical mechanics. No
accumulation of excitation occurs in the large scales, even though in the
dissipative rotating case anisotropy and accumulation, in the form of an
inverse cascade of energy, are known to occur. We attribute this latter
discrepancy to the linearity of the term responsible for the emergence of
inertial waves. At intermediate times, inertial energy spectra emerge that
differ somewhat from classical wave-turbulence expectations, and with a trace
of large-scale excitation that goes away for long times. These results are
discussed in the context of partial two-dimensionalization of the flow
undergoing strong rotation as advocated by several authors.
