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We consider the flow of a Newtonian fluid in a three-dimensional domain,rotating about a vertical axis and driven by a vertically invariant horizontalbody-force. This system admits vertically invariant solutions that satisfy the2D Navier-Stokes equation. At high Reynolds number and without global rotation,such solutions are usually unstable to three-dimensional perturbations. Bycontrast, for strong enough global rotation, we prove rigorously that the 2D(and possibly turbulent) solutions are stable to vertically dependentperturbations: the flow becomes 2D in the long-time limit.  These results shed some light on several fundamental questions of rotatingturbulence: for arbitrary Reynolds number and small enough Rossby number, thesystem is attracted towards purely 2D flow solutions, which display no energydissipation anomaly and no cyclone-anticyclone asymmetry. Finally, theseresults challenge the applicability of wave turbulence theory to describestationary rotating turbulence in bounded domains.

Exact two-dimensionalization of rapidly rotating large-Reynolds-number flows