Zonostrophic turbulence and interactions with a stratified layer

Owing to the action of the Coriolis force, convection in planetary cores is strongly affected by the rapid rotation of the planet. Even if the convective flows are turbulent, the fast rotation results in a dynamical balance between the Coriolis force and the horizontal pressure gradient called the geostrophic balance. This balance implies a bidimensionalization of the flow with invariance along the rotation axis, resulting in columnar structures parallel to the rotation axis. However, planetary core convective flows are not purely 2-D and are significantly affected by three dimensional effects, that is why such flows are commonly described using the so-called "quasi-geostrophic approximation" (QGA).

In the QGA framework, the Coriolis force creates a Beta-effect due to the variation of the fluid column height with the distance to the rotation axis. This effect, when present among a quasi-2D turbulent flow, drives strong zonal mean flows corresponding to concentric cylinders of alternating rotating directions, that is successively westward and eastward. The observation of such zonal jets in geophysical and astrophysical objects has strongly motivated their study. Notably, zonal jets are observed in gas giants' atmospheres, Earth's ocean and atmosphere, as well as exoplanets and the Sun. All of these systems belong to the same generic framework of quasi-geostrophic turbulence affected by a beta-effect to which we refer as zonostrophic tubulence.

Several open questions remain regarding zonal jets among turbulent flows. We address experimentally the questions of the physical origin of the zonal jets, their size and intensity, as well as their long-term evolution and interaction with the rapidly fluctuating turbulent flow. Reproducing jets in the zonostrophic regime is experimentally challenging, namely because of large boundary dissipation and small β-effect. Recently, Cabanes et al. (2017) built an experimental setup allowing the formation of zonal flows which were closer to planetary regimes than any previous experiment. Afterwards, we built a significantly improved version of this setup which, among other differences, allows us to perform time-resolving particle image velocimetry (PIV) measurements. In this setup, the variation of the fluid height responsible for the β-effect is the one induced by the rapid rotation (75 rounds per minute) of a cylindrical water-filled tank, i.e. a parabolic increase of the fluid height with radius. A small-scale forcing is performed using submersible pumps which circulates the tank's water through a polar array of 128 injection and suction points located at the base of the tank. From this forcing, the flow self-organizes at large scale into zonal jets. In a recent study (Lemasquerier et al., submitted), we identified two jets regimes, the transition from one another being due to the resonance of the Reynolds stresses driving the zonal flow with the mean flow itself.

In addition to this experimental study, we use idealized numerical simulations to explore the parameters space and to study extreme regimes that are not reachable experimentally, such as larger β-effects or smaller friction which would require too high rotation rates. For that purpose, we use a quasi-gestrophic (QG) model which takes advantage of the bidimensionalization of the flow due to rotation.

Finally, we aim at adding a stratified layer at the top of the fluid to study the coupled dynamics between the zonostrophic turbulence and the stratified layer at the surface which would mimic Jupiter's weather layer into which are embedded the vortices observed on Jupiter.

References

• Kaspi, Y., Galanti, E., Hubbard, W. et al. Jupiter’s atmospheric jet streams extend thousands of kilometres deep. Nature 555, 223–226 (2018).
• Cabanes, S., Aurnou, J., Favier, B., and Le Bars, M. A laboratory model for deep-seated jets on the gas giants. Nature Physics, 13(4):387, 2017.
• Lemasquerier, D., Favier, B., and Le Bars, M. Zonal jets at the laboratory scale: hysteresis and Rossby waves resonance. Submitted to Journal of Fluid Mechanics on May 18, 2020.