Large-scale behavior and statistical equilibria in rotating flows.

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, although, 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.