## 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

*Friday, March 30, 20181:30 p.m.*

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.