Inverse cascades and resonant triads in rotating and stratified turbulence

Abstract

Kraichnan 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 ratio $N/f$ of the Brunt-Väisäla frequency to the Coriolis 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, $1/2\le N/f\le 2$. We then use the spatio-temporal spectrum, and characterization of the flow temporal and spatial scales, 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.

17 pages, 13 figures, new version has all changes in the paper published in the Two Dimensional Turbulence Focus Issue of Physics of Fluids

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• Experimental study of the non-linear saturation of the elliptical instability: inertial wave turbulence versus geostrophic turbulence
• The effect of rotation on fingering convection in stellar interiors
• Energy cascades in rapidly rotating and stratified turbulence within elongated domains
• Near Resonant Approximation of the Rotating Stratified Boussinesq system on a 3-Torus
• Dynamic Triad Interactions and Evolving Turbulence -- Part 2: Implications for Practical Signals
• Effects of Rotation on Vorticity Dynamics on a Sphere with Discrete Exterior Calculus