Interplay of waves and eddies in rotating stratified turbulence and the link with kinetic-potential energy partition

¹ École Normale Supérieure de Lyon, Université de Lyon - Lyon F-69007, France
² Space Sciences Laboratory, University of California Berkeley - Berkeley, CA 94720, USA
³ National Center for Computational Sciences, Oak Ridge National Laboratory - Oak Ridge, TN 37831, USA
⁴ SciTec, Inc., Princeton - NJ 08540, USA
⁵ Department of Physics of Complex Systems, Weizmann Institute of Science - Rehovot 76100, Israel
⁶ Laboratory for Atmospheric and Space Physics, University of Colorado - Boulder, CO 80309, USA
⁷ National Center for Atmospheric Research - Boulder, CO 80307, USA

Received: 9 November 2015
Accepted: 10 November 2015

Abstract

The interplay between waves and eddies in stably stratified rotating flows is investigated by means of world-class direct numerical simulations using up to 3072³ grid points. Strikingly, we find that the shift from vortex- to wave-dominated dynamics occurs at a wave number k_R which does not depend on the Reynolds number, suggesting that the partition of energy between wave and vortical modes is not sensitive to the development of turbulence at the smaller scales. We also show that k_R is comparable to the wave number at which exchanges between kinetic and potential modes stabilize at close to equipartition, emphasizing the role of potential energy, as conjectured in the atmosphere and the oceans. Moreover, k_R varies as the inverse of the Froude number as explained by the scaling prediction proposed, consistently with recent observations and modeling of the Mesosphere–Lower Thermosphere and of the ocean.