Some statistical properties of three-dimensional zonostrophic turbulence

S. Cabanes (1) , B. Favier (1) , M. Le Bars (1)

1 IRPHE - Institut de Recherche sur les Phénomènes Hors Equilibre

We conduct in-depth analysis of statistical flow properties from direct numerical simulations that reproduce gas giants macroturbulence, namely large-scale zonal winds. Our numerical model has been specifically designed to simulate a recent laboratory device that reports zonal jets in the configuration of deep turbulent planetary layers. In this framework, the so-called zonostrophic regime is achieved when large topographical variations of the fluid layer combine with rapid rotation in a well developed three-dimensional (3D) turbulent flow. At steady state, strongly energetic, zonally dominated, large-scale axisymmetric structures emerge scaling with Rhines’ theoretical scale. This model differs from the shallow-layer scenario where the flow is confined to a quasi-two-dimensional (2D) fluid shell and the anisotropic β-effect arises from latitudinal variation of the Coriolis force. Thus, we aim to reveal, in the specific framework of the deep-layer scenario, signatures of the zonostrophic regime and of a β-topography in statistical flow properties. To do so, we run two large-scale 3D direct numerical simulations in a cylindrical geometry of a highly turbulent and rapidly rotating flow. These two simulations use similar set of parameters but with and without topographical β-effect. We propose a comparative phenomenological description of the temporal and spatial statistics of the three components of the velocity field. Interestingly, we report that peculiar correlations occur between the vertical and radial flow components when a β-topography is imposed and show a feature possibly due to a zonostrophic dynamics in 3D frequency spectra. These results suggest the development of new tools to remotely investigate gas giants zonal winds by extracting statistical flow properties from direct observations. Ultimately our analysis may support the relevance of the deep models in the study of prevalent features of planetary dynamics.

Mots clés: Zonostrophic turbulence; zonal jets

Domaines: Physique de l'espace [physics.space-ph]; Astrophysique [astro-ph]

S. Cabanes, B. Favier, M. Le Bars. Some statistical properties of three-dimensional zonostrophic turbulence. Geophysical and Astrophysical Fluid Dynamics, 2018, 112 (3), pp.207-221. ⟨10.1080/03091929.2018.1467413⟩. ⟨hal-01904597⟩