Title: 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.