Inverse cascades in rotating stratified turbulence: Fast growth of large scales

¹ National Center for Atmospheric Research - P.O. Box 3000, Boulder, CO 80307, USA
² Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and IFIBA, CONICET - Ciudad Universitaria, 1428 Buenos Aires, Argentina
³ National Center for Computational Sciences, Oak Ridge National Laboratory P.O. Box 2008, Oak Ridge, TN 37831, USA
⁴ Department of Applied Mathematics, University of Colorado at Boulder - Boulder, CO 80309, USA

Received: 11 March 2013
Accepted: 17 May 2013

Abstract

We examine the inverse cascade of kinetic energy to large scales in rotating stratified turbulence as occurs in the oceans and in the atmosphere, while varying the relative frequency of gravity to inertial waves, N/f. Using direct numerical simulations with grid resolutions up to 1024³ points, we find that the transfer of energy from three-dimensional to two-dimensional modes is most efficient in the range 1/2 ⩽ N/f ⩽ 2, in which resonances disappear. In this range, the cascade is faster than in the purely rotating case, and thus the interplay between rotation and stratification helps creating large-scale structures. The ensuing inverse cascade follows a −5/3 spectral law with an approximately constant flux. This inverse cascade becomes negligible when stratification is dominant.