Turbulence and waves in the presence of rotation and stratification*

Annick Pouquet,Research Scientist, Laboratory for Atmospheric and Space Physics, Boulder CO, Senior Scientist Emeritus, CISL/NCAR

Hopeman 224

In the atmosphere and the oceans, turbulence is strong at the smallest scales whereas waves
dominate large-scale dynamics, influencing the effective energy dissipation: in rotating
stratified turbulence (RST) in the Boussinesq framework, velocity couples to density fluctuations
and the system supports inertia-gravity waves, with an anisotropic dispersion relation. What
kind of turbulence regimes result from the interactions between nonlinear eddies and waves in
such flows? And what is delimiting these regimes? Two specific examples will be analyzed
below: strength (i) of energy dissipation and the mixing properties of the fluid, and (ii) of energy
cascades.
I shall sketch the phenomenological framework within which one is led to simple scaling laws in
Froude number Fr for the mixing, in terms of flux Richardson number and for related expressions
measuring the relative roles of the buoyancy flux due to the waves, and of the measured rates of
kinetic and potential energy dissipation. Using β as the effective rate of kinetic energy dissipation
compared to its dimensional estimate, we find that β scales as the Froude number Fr, that is the
ratio of the gravity wave period to the eddy turn-over time [1,2]. This defines an intermediate
regime bridging the gap between the strong-wave and the strong-eddy regimes in such flows.
This corroborates results from other numerical data sets, as well as from recent atmospheric
and oceanic observations.
If time permits, I will also describe results using forced numerical simulations for RST showing
that a dual cascade of energy can be observed, towards both small and large scales and in both
cases with constant fluxes [2]. The scaling of the strength of the inverse relative to the direct
constant energy fluxes is obtained through a simple modeling of wave-eddy interactions that
relies on the efficiency of the cascade to small scales and which is compatible with the previous
findings of dissipation efficiency in the decay case.
* NCAR/NSF ASD allocation for a large parametric study of RST, on grids of 5123, 10243 and
20483 points.
[1] AP, D. Rosenberg, R. Marino & C. Herbert, Scaling laws for mixing and dissipation in
unforced rotating stratified turbulence. To appear, J. Fluid Mechanics, ArXiv Physics.fludyn/
1708.07146v2, 2018.
[2] R. Marino, AP & D. Rosenberg, Resolving the paradox of oceanic large-scale balance and
small-scale mixing. Physical Review Letters 114, 114504, 2015.