Effects of Inertiogravity Waves and Rotation on Two-Dimensional Turbulence

Abstract

We are studying the interactions between rotational eddies and inertio-gravity waves in a uniformly rotating shallow fluid layer, and the associated spectra and cascades, in order to understand the mechanisms generating geostrophy, i.e., the balance between the wind and mass fields in large-scale geophysical flows. We first derive the statistical equilibrium states in the inviscid limit, to get a preliminary understanding of the physical processes involved when inertio-gravity waves are present, and this independently of any parameterization of the small-scale behavior. We then study the turbulent flow regimes without forcing, considering different initial amounts of inertio-gravity waves and geostrophic eddies, and three different rotation rates. We find that, for low rotation rates, inertio-gravity waves induce an energy dissipation, in contrast to the nondissipative behavior of incompressible turbulence. But, for high rotation rates, there is no more energy dissipation, and inertiogravitational energy, like rotational energy, remains confined in the larger scales. If inertio-gravity waves are only weakly excited, rotation inhibits both the direct potential enstrophy cascade and the inverse rotational energy cascade. We also observe that, when rotation is increased, there is no more tendency towards quasigeostrophic adjustment because of the strong excitation of inertial waves trapped at large scales. Copyright © 1988 by Marie Farge, Published by the American Institute of Aeronautics and Astronautics, Inc. with permission. *Laboratoire de Meteorologie Dynamique, 355