International audienceIn this paper we present numerical simulations of rapidly-rotating Rayleigh-Bénard convection in the Boussi-nesq approximation with stress-free boundary conditions. At moderately low Rossby number and large Rayleigh number, we show that a large-scale depth-invariant flow is formed, reminiscent of the condensate state observed in two-dimensional flows. We show that the large-scale circulation shares many similarities with the so-called vortex, or slow-mode, of forced rotating turbulence. Our investigations show that at a fixed rotation rate the large-scale vortex is only observed for a finite range of Rayleigh numbers, as the quasi-two-dimensional nature of the flow disappears at very high Rayleigh numbers. We observe slow vortex merging events and find a non-local inverse cascade of energy in addition to the regular direct cascade associated with fast small-scale turbulent motions. Finally, we show that cyclonic structures are dominant in the small-scale turbulent flow and this symmetry breaking persists in the large-scale vortex motion

We study the evolution of a melting front between the solid and liquid phases of a pure incompressible material where fluid motions are driven by unstable temperature gradients. In a plane layer geometry, this can be seen as classical Rayleigh-Bénard convection where the upper solid boundary is allowed to melt due to the heat flux brought by the fluid underneath. This free-boundary problem is studied numerically in two dimensions using a phase-field approach, classically used to study the melting and solidification of alloys, which we dynamically couple with the Navier-Stokes equations in the Boussinesq approximation. The advantage of this approach is that it requires only moderate modifications of classical numerical methods. We focus on the case where the solid is initially nearly isothermal, so that the evolution of the topography is related to the inhomogeneous heat flux from thermal convection, and does not depend on the conduction problem in the solid. From a very thin stable layer of fluid, convection cells appears as the depth-and therefore the effective Rayleigh number-of the layer increases. The continuous melting of the solid leads to dynamical transitions between different convection cell sizes and topography amplitudes. The Nusselt number can be larger than its value for a planar upper boundary, due to the feedback of the topography on the flow, which can stabilize large-scale laminar convection cells. †

We perform one of the first studies into the nonlinear evolution of tidally excited inertial waves in a uniformly rotating fluid body, exploring a simplified model of the fluid envelope of a planet (or the convective envelope of a solar-type star) subject to the gravitational tidal perturbations of an orbiting companion. Our model contains a perfectly rigid spherical core, which is surrounded by an envelope of incompressible uniform density fluid. The corresponding linear problem was studied in previous papers which this work extends into the nonlinear regime, at moderate Ekman numbers (the ratio of viscous to Coriolis accelerations). By performing high-resolution numerical simulations, using a combination of pseudo-spectral and spectral element methods, we investigate the effects of nonlinearities, which lead to time-dependence of the flow and the corresponding dissipation rate. Angular momentum is deposited non-uniformly, leading to the generation of significant differential rotation in the initially uniformly rotating fluid, i.e. the body does not evolve towards synchronism as a simple solid body rotator. This differential rotation modifies the properties of tidally excited inertial waves, changes the dissipative properties of the flow, and eventually becomes unstable to a secondary shear instability provided that the Ekman number is sufficiently small. Our main result is that the inclusion of nonlinearities eventually modifies the flow and the resulting dissipation from what linear calculations would predict, which has important implications for tidal dissipation in fluid bodies. We finally discuss some limitations of our simplified model, and propose avenues for future research to better understand the tidal evolution of rotating planets and stars.

We analyze the anisotropy of turbulence in an electrically conducting fluid in the presence of a uniform magnetic field, for low magnetic Reynolds number, using the quasi-static approximation. In the linear limit, the kinetic energy of velocity components normal to the magnetic field decays faster than the kinetic energy of component along the magnetic field [Moffatt, JFM 28, 1967]. However, numerous numerical studies predict a different behavior, wherein the final state is characterized by dominant horizontal energy. We investigate the corresponding nonlinear phenomenon using Direct Numerical Simulations. The initial temporal evolution of the decaying flow indicates that the turbulence is very similar to the so-called "two-and-a-halfdimensional" flow [Montgomery & Turner, Phys. Fluids 25(2), 1982] and we offer an explanation for the dominance of horizontal kinetic energy.

Longitudinal libration corresponds to the periodic oscillation of a body’s rotation rate and is, along with precessional and tidal forcings, a possible source of mechanically-driven turbulence in the fluid interior of satellites and planets. In this study, we present a combination of direct numerical simulations and laboratory experiments, modeling this geophysically relevant mechanical forcing. We investigate the fluid motions inside a longitudinally librating ellipsoidal container filled with an incompressible fluid. The elliptical instability, which is a triadic resonance between two inertial modes and the oscillating base flow with elliptical streamlines, is observed both numerically and experimentally. The large-scale inertial modes eventually lead to small-scale turbulence, provided that the Ekman number is small enough. We characterize this transition to turbulence as additional triadic resonances develop while also investigating the properties of the turbulent flow that displays both intermittent and sustained regimes. These turbulent flows may play an important role in the thermal and magnetic evolution of bodies subject to mechanical forcing, which is not considered in standard models of convectively driven magnetic field generation.

The combination of elliptical deformation of streamlines and vorticity can lead to the destabilization of any rotating flow via the elliptical instability. Such a mechanism has been invoked as a possible source of turbulence in planetary cores subject to tidal deformations. The saturation of the elliptical instability has been shown to generate turbulence composed of nonlinearly interacting waves and strong columnar vortices with varying respective amplitudes, depending on the control parameters and geometry. In this Letter, we present a suite of numerical simulations to investigate the saturation and the transition from vortex-dominated to wave-dominated regimes. This is achieved by simulating the growth and saturation of the elliptical instability in an idealized triply periodic domain, adding a frictional damping to the geostrophic component only, to mimic its interaction with boundaries. We reproduce several experimental observations within one idealized local model and complement them by reaching more extreme flow parameters. In particular, a wave-dominated regime that exhibits many signatures of inertial wave turbulence is characterized for the first time. This regime is expected in planetary interiors.

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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...