Highlights• A new Global Climate Model for Saturn with radiative transfer • High-resolution numerical simulations on a duration of 15 Saturn years • Results on zonal jets, waves, eddies in Saturn's troposphere AbstractThe Cassini mission unveiled the intense and diverse activity in Saturn's atmosphere: banded jets, waves, vortices, equatorial oscillations. To set the path towards a better understanding of those phenomena, we performed high-resolution multi-annual numerical simulations of Saturn's atmospheric dynamics. We built a new Global Climate Model [GCM] for Saturn, named the Saturn DYNAMICO GCM, by combining a radiative-seasonal model tailored for Saturn to a hydrodynamical solver based on an icosahedral grid suitable for massively-parallel architectures. The impact of numerical dissipation, and the conservation of angular momentum, are examined in the model before a reference simulation employing the Saturn DYNAMICO GCM with a 1/2 • latitude-longitude resolution is considered for analysis. Mid-latitude banded jets showing similarity with observations are reproduced by our model. Those jets are accelerated and maintained by eddy momentum transfers to the mean flow, with the magnitude of momentum fluxes compliant with the observed values. The eddy activity is not regularly distributed with time, but appears as bursts; both barotropic and baroclinic instabilities could play a role in the eddy activity. The steady-state latitude of occurrence of jets is controlled by poleward migration during the spin-up of our model. At the equator, a weaklysuperrotating tropospheric jet and vertically-stacked alternating stratospheric jets are obtained in our GCM simulations. The model produces Yanai (Rossby-gravity), Rossby and Kelvin waves at the equator, as well as extratropical Rossby waves, and large-scale vortices in polar regions. Challenges remain to reproduce Saturn's powerful superrotating jet and hexagon-shaped circumpolar jet in the troposphere, and downward-propagating equatorial oscillation in the stratosphere.

The strong east-west jet flows on the gas giants, Jupiter Azimuthally directed (that is, zonal, east-west) jet flows are one of the dominant characteristics in the surficial cloud features observed on the gas giants, Jupiter and Saturn. An essential question of planetary dynamics and structure is whether these jet motions exist only within the shallow troposphere or extend through the molecular envelope that exists above the deeper dynamo region 3 . Determining the depth of these atmospheric jets is one of the prime directives of the NASA (National Aeronautics and Space Administration) Juno mission, which entered into low-altitude Jovian orbit in August 2016 4 . Despite the long-lived scientific interest in these flows, dominant multiple jets have been problematic in fully three-dimensional (3D) numerical models of convection. In particular, multiple banded flows are not found in the most recent, high-resolution models that couple the molecular envelope to the deeper dynamo region. In these models, magnetic dissipation damps the higher-latitude deep jets out of existence [5][6][7] . Similarly, dissipation has also proved overly important in laboratory experiments carried out to date. Laboratory approaches were analysed in the framework of the shallow-layer model and strong viscous damping by the container boundaries only allows for the formation of weak zonal jets with tenuous instantaneous signatures [8][9][10][11][12][13][14] . Thus, it has yet to be demonstrated, as proposed for the gas giant planets 15 , that deep zonally dominant jet flows can exist in the presence of boundary dissipation.We have developed a new laboratory experimental device that is capable of generating strong zonal jets despite viscous friction on the boundaries (Fig. 1a). The working fluid is water, contained in a 1.37-m-high by 1-m-diameter cylindrical tank. The depth of the fluid layer is h o = 50 cm at rest, and the tank's rotation rate is Ω = 7.85 rad s −1 (75 revolutions per minute). Once equilibrated at Ω, the water's free surface takes the shape of a paraboloid, with the fluid layer depth ranging from h min 20 cm on the axis of rotation to h max 90 cm at the tank's outer radius. This rotating surface shape is analogous to the large-scale curvature of a deep spherical planetary fluid layer 16,17 . In addition, the rotation provides strong Coriolis forces, as exist in planetary settings. Once solid body rotation is reached, a submersible pump situated at the base of the tank is turned on, and small-scale turbulence is injected at the base of the fluid layer. The pump continuously circulates water through a lattice of 32 outlets (4 mm diameter) and 32 inlets (2 mm diameter) arranged on a flat base plate without any axisymmetric features (see the injection pattern in Supplementary Fig. 1a). Typical root-mean-square (r.m.s.) fluctuating velocities are in the range u r.m.s. 1-5 cm s −1 . This small-scale turbulence is analogous to the convective turbulence that exists in deep planetary interiors 18,19 and constitutes an appropriate s...

We conduct an in-depth analysis of statistical flow properties calculated from the reference high-resolution Saturn simulation obtained by global climate modelling in Part II. In the steady state of this reference simulation, strongly energetic, zonally dominated, large-scale structures emerge, which scale with the Rhines scale. Spectral analysis reveals a strong anisotropy in the kinetic energy spectra, consistent with the zonostrophic turbulent flow regime. By computing spectral energy and enstrophy fluxes we confirm the existence of a double cascade scenario related to 2D-turbulent theory. To diagnose the relevant 3D dynamical mechanisms in Saturn's turbulent atmosphere, we run a set of four simulations using an idealized version of our Global Climate Model devoid of radiative transfer, with a well-defined Taylor-Green forcing and over several rotation rates (4, 1, 0.5, and 0.25 times Saturn's rotation rate). This allows us to identify dynamics in three distinctive inertial ranges: (1) a "residual-dominated" range, in which non-axisymmetric structures dominate with a −5/3 spectral slope; (2) a "zonostrophic inertial" range, dominated by axisymmetric jets and characterized by the pile-up of strong zonal modes with a steeper, nearly −3, spectral slope; and (3) a "large-scale" range, beyond Rhines' typical length scale, in which the reference Saturn simulation and our idealized simulations differ. In the latter range, the dynamics is dom- * Corresponding author. inated by long-lived zonal modes 2 and 3 when a Saturn-like seasonal forcing is considered (reference simulation), and a steep energetic decrease with the idealized Taylor-Green forcing. Finally, instantaneous spectral fluxes show the coexistence of upscale and downscale enstrophy/energy transfers at large scales, specific to the regime of zonostrophic turbulence in a 3D atmosphere.

The Composite InfraRed Spectrometer (CIRS) on board Cassini revealed an equatorial oscillation of stratospheric temperature, reminiscent of the Earth's Quasi-Biennial Oscillation (QBO), as well as anomalously high temperatures under Saturn's rings. To better understand these predominant features of Saturn's atmospheric circulation in the stratosphere, we have extended to the upper stratosphere the DYNAMICO-Saturn global climate model (GCM), already used in a previous publication to study the tropospheric dynamics, jets formation and planetary-scale waves activity. Firstly, we study the higher model top impact on the tropospheric zonal jets and kinetic energy distribution. Raising the model top prevents energy and enstrophy accumulation at tropopause levels. The reference GCM simulation with 1/2 • latitude/longitude resolution and a raised model top exhibits a QBO-like oscillation produced by resolved planetary-scale waves. However, the period is more irregular and the downward propagation faster than observations. Furthermore, compared to the CIRS temperature retrievals, the modeled QBO-like oscillation underestimates by half both the amplitude of temperature anomalies at the equator and the vertical characteristic length of this equatorial oscillation. This QBO-like oscillation is mainly driven by westward-propagating waves; a significant lack of eastward waveforcing explains a fluctuating eastward phase of the QBO-like oscillation. We also show that the seasonal cycle of Saturn is a key parameter of the establishment and the regularity of the equatorial oscillation. At 20 • N and 20 • S latitudes, the DYNAMICO-Saturn GCM exhibits several strong seasonal eastward jets, alternatively in the northern and southern hemisphere. These jets are correlated with the rings' shadowing. Using a GCM simulation without rings' shadowing, we show its impact on Saturn's stratospheric dynamics. Both residualmean circulation and eddy forcing are impacted by rings' shadowing. In particular, the QBO-like oscillation is weakened by an increased drag caused by those two changes associated with rings' shadowing.

The contribution of small scale turbulent fluctuations to the induction of mean magnetic field is investigated in our liquid sodium spherical Couette experiment with an imposed magnetic field. An inversion technique is applied to a large number of measurements at Rm ≈ 100 to obtain radial profiles of the α and β effects and maps of the mean flow. It appears that the small scale turbulent fluctuations can be modeled as a strong contribution to the magnetic diffusivity that is negative in the interior region and positive close to the outer shell. Direct numerical simulations of our experiment support these results. The lowering of the effective magnetic diffusivity by small scale fluctuations implies that turbulence can actually help to achieve self-generation of large scale magnetic fields.The Earth, the Sun and many other astrophysical bodies produce their own magnetic field by dynamo action, where the induction of a magnetic field by fluid motion overcomes the Joule dissipation. In all astrophysical bodies, the conducting fluid undergoes turbulent motions, which can also significantly affect the induction of a largescale magnetic field by either enhancing it or weakening it. It is therefore of primary interest to quantify the role of these fluctuations in the dynamo problem.The induction equation for the mean magnetic field B reads:where U is the mean velocity field, η = (µ 0 σ) −1 is the magnetic diffusivity (involving the magnetic permeability µ 0 and the conductivity of the fluid σ), and E = ũ ×b is the mean electromotive force (emf) due to small scale fluctuating magneticb and velocityũ fields. The relative strength between the inductive and dissipative effects is given by the magnetic Reynolds number Rm = U L/η (U and L are characteristic velocity and the characteristic length-scale). When there is a scale separation between the turbulent fluctuations and the mean flow, we can follow the mean-field theory and expand the emf in terms of mean magnetic quantities: E = α B − β∇ × B . For homogeneous isotropic turbulence, α and β are scalar quantities. α is related to the flow helicity and results in an electrical current aligned with the mean magnetic field, whereas β can be interpreted as a turbulent diffusivity effectively increasing (β > 0) or decreasing (β < 0) electrical currents. The effective magnetic diffusivity η ef f = η + β can have tremendous effects on energy dissipation and on dynamo action by reducing or increasing the effective magnetic Reynolds number Rm ef f = U L/η ef f .However, direct determination of these small-scale contributions remains a challenging issue for experimental studies and numerical simulations.The first generation of dynamo experiments were designed to show that turbulent flows with strong geometrically-imposed helicity could self-generate their own magnetic fields. Since the success of Riga [1] and Karlsruhe [2] dynamos, several other liquid metal experiments have sought to overcome the effects of magnetohydrodynamic turbulence in less constrained, more geophysically rele...

We present a reconstruction of the mean axisymmetric azimuthal and meridional flows in the DTS liquid sodium experiment. The experimental device sets a spherical Couette flow enclosed between two concentric spherical shells where the inner sphere holds a strong dipolar magnet, which acts as a magnetic propeller when rotated. Measurements of the mean velocity, mean induced magnetic field and mean electric potentials have been acquired inside and outside the fluid for an inner sphere rotation rate of 9 Hz (Rm 28). Using the induction equation to relate all measured quantities to the mean flow, we develop a nonlinear least square inversion procedure to reconstruct a fully coherent solution of the mean velocity field. We also include in our inversion the response of the fluid layer to the non-axisymmetric time-dependent magnetic field that results from deviations of the imposed magnetic field from an axial dipole. The mean azimuthal velocity field we obtain shows super-rotation in an inner region close to the inner sphere where the Lorentz force dominates, which contrasts with an outer geostrophic region governed by the Coriolis force, but where the magnetic torque remains the driver. The meridional circulation is strongly hindered by the presence of both the Lorentz and the Coriolis forces. Nevertheless, it contributes to a significant part of the induced magnetic energy. Our approach sets the scene for evaluating the contribution of velocity and magnetic fluctuations to the mean magnetic field, a key question for dynamo mechanisms.

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 (Cabanes et al. 2017). 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 shallowlayer scenario where the flow is confined to a quasi-two-dimensional (2D) fluid shell and the anisotropic βeffect 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.

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