Kraichnan’s seminal ideas on inverse cascades yielded new tools to study common phenomena in geophysical turbulent flows. In the atmosphere and the oceans, rotation and stratification result in a flow that can be approximated as two-dimensional at very large scales but which requires considering three-dimensional effects to fully describe turbulent transport processes and non-linear phenomena. Motions can thus be classified into two classes: fast modes consisting of inertia-gravity waves and slow quasi-geostrophic modes for which the Coriolis force and horizontal pressure gradients are close to balance. In this paper, we review previous results on the strength of the inverse cascade in rotating and stratified flows and then present new results on the effect of varying the strength of rotation and stratification (measured by the inverse Prandtl ratio N/f, of the Coriolis frequency to the Brunt-Väisäla frequency) on the amplitude of the waves and on the flow quasi-geostrophic behavior. We show that the inverse cascade is more efficient in the range of N/f for which resonant triads do not exist, . We then use the spatio-temporal spectrum to show that in this range slow modes dominate the dynamics, while the strength of the waves (and their relevance in the flow dynamics) is weaker.
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November 2017
Research Article|
September 14 2017
Inverse cascades and resonant triads in rotating and stratified turbulence
D. Oks
;
D. Oks
1
Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Departamento de Física, and IFIBA, CONICET, Ciudad Universitaria
, Buenos Aires 1428, Argentina
2
Laboratoire de Physique–UMR 5672, Ecole Normale Supérieure de Lyon, CNRS
, 46 Allée d’Italie, 69007 Lyon, France
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P. D. Mininni;
P. D. Mininni
1
Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Departamento de Física, and IFIBA, CONICET, Ciudad Universitaria
, Buenos Aires 1428, Argentina
3
NCAR
, P.O. Box 3000, Boulder, Colorado 80307-3000, USA
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R. Marino
;
R. Marino
4
Laboratoire de Mécanique des Fluides et d’Acoustique, CNRS, École Centrale de Lyon, Université de Lyon
, 69134 Écully, France
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A. Pouquet
A. Pouquet
3
NCAR
, P.O. Box 3000, Boulder, Colorado 80307-3000, USA
5
Laboratory for Atmospheric and Space Physics, University of Colorado
, Boulder, Colorado 80309-256, USA
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Physics of Fluids 29, 111109 (2017)
Article history
Received:
April 24 2017
Accepted:
August 23 2017
Citation
D. Oks, P. D. Mininni, R. Marino, A. Pouquet; Inverse cascades and resonant triads in rotating and stratified turbulence. Physics of Fluids 1 November 2017; 29 (11): 111109. https://doi.org/10.1063/1.5001740
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