Céline Guervilly

Large-scale vortices in rapidly rotating Rayleigh–Bénard convection

Using numerical simulations of rapidly rotating Boussinesq convection in a Cartesian box, we study the formation of long-lived, large-scale, depth-invariant coherent structures. These structures, which consist of concentrated cyclones, grow to the horizontal scale of the box, with velocities significantly larger than the convective motions. We vary the rotation rate, the thermal driving and the aspect ratio in order to determine the domain of existence of these large-scale vortices (LSV). We find that two conditions are required for their formation. First, the Rayleigh number, a measure of the thermal driving, must be several times its value at the linear onset of convection; this corresponds to Reynolds numbers, based on the convective velocity and the box depth, ≳100. Second, the rotational constraint on the convective structures must be strong. This requires that the local Rossby number, based on the convective velocity and the horizontal convective scale, ≲0.15. Simulations in which certain wavenumbers are artificially suppressed in spectral space suggest that the LSV are produced by the interactions of small-scale, depth-dependent convective motions. The presence of LSV significantly reduces the efficiency of the convective heat transport.

Numerical simulations of dynamos generated in spherical Couette flows

We numerically investigate the efficiency of a spherical Couette flow at generating a self-sustained magnetic field. No dynamo action occurs for axisymmetric flow, while we always found a dynamo when non-axisymmetric hydrodynamical instabilities are excited. Without rotation of the outer sphere, typical critical magnetic Reynolds numbers Rm c are of the order of a few thousands. They increase as the mechanical forcing imposed by the inner core on the flow increases (Reynolds number Re). Namely, no dynamo is found if the magnetic Prandtl number Pm = Rm/Re is less than a critical value Pm c ∼ 1. Oscillating quadrupolar dynamos are present in the vicinity of the dynamo onset. Saturated magnetic fields obtained in supercritical regimes (either Re > 2Re c or Pm > 2Pm c ) correspond to the equipartition between magnetic and kinetic energies. A global rotation of the system (Ekman numbers E = 10−3, 10−4) yields to a slight decrease (factor 2) of the critical magnetic Prandtl number, but we find a peculiar regime where dynamo action may be obtained for relatively low magnetic Reynolds numbers (Rm c ∼ 300). In this dynamical regime (Rossby number Ro ∼ −1, spheres in opposite direction) at a moderate Ekman number (E = 10−3), an enhanced shear layer around the inner core might explain the decrease of the dynamo threshold. For lower E (E = 10−4) this internal shear layer becomes unstable, leading to small scale fluctuations, and the favorable dynamo regime is lost. We also model the effect of ferromagnetic boundary conditions. Their presence have only a small impact on the dynamo onset, but clearly enhance the saturated magnetic field in the ferromagnetic parts. Implications for experimental studies are discussed.

Generation of magnetic fields by large-scale vortices in rotating convection.

We propose a self-consistent dynamo mechanism for the generation of large-scale magnetic fields in natural objects. Recent computational studies have described the formation of large-scale vortices in rotating turbulent convection. Here we demonstrate that for magnetic Reynolds numbers below the threshold for small-scale dynamo action, such turbulent flows can sustain large-scale magnetic fields, i.e., fields with a significant component on the scale of the system.

The Rotation Rate of the Solar Radiative Zone

The rotation rate of the solar radiative zone is an important diagnostic for angular momentum transport in the tachocline and below. In this paper, we study the contribution of viscous and magnetic stresses to the global angular momentum balance. By considering a simple linearized toy model, we discuss the effects of field geometry and applied boundary conditions on the predicted rotation profile and rotation rate of the radiative interior. We compare these analytical predictions with fully nonlinear simulations of the dynamics of the radiative interior, as well as with observations. We discuss the implications of these results as constraints on models of the solar interior.

A dynamo driven by zonal jets at the upper surface : applications to giant planets

We present a dynamo mechanism arising from the presence of barotropically unstable zonal jet currents in a rotating spherical shell. The shear instability of the zonal flow develops in the form of a global Rossby mode, whose azimuthal wavenumber depends on the width of the zonal jets. We obtain self-sustained magnetic fields at magnetic Reynolds numbers greater than 1000. We show that the propagation of the Rossby waves is crucial for dynamo action. The amplitude of the axisymmetric poloidal magnetic field depends on the wavenumber of the Rossby mode, and hence on the width of the zonal jets. We discuss the plausibility of this dynamo mechanism for generating the magnetic field of the giant planets. Our results suggest a possible link between the topology of the magnetic field and the profile of the zonal winds observed at the surface of the giant planets. For narrow Jupiter-like jets, the poloidal magnetic field is dominated by an axial dipole whereas for wide Neptune-like jets, the axisymmetric poloidal field is weak.

Subcritical convection of liquid metals in a rotating sphere using a quasi-geostrophic model

We study nonlinear convection in a rapidly rotating sphere with internal heating for values of the Prandtl number relevant for liquid metals (

Jets and large-scale vortices in rotating Rayleigh-Bénard convection

Pr\in[10^{-2},10^{-1}]

Large-scale-vortex dynamos in planar rotating convection

). We use a numerical model based on the quasi-geostrophic approximation, in which variations of the axial vorticity along the rotation axis are neglected, whereas the temperature field is fully three-dimensional. We identify two separate branches of convection close to onset: (i) a well-known weak branch for Ekman numbers greater than

Self-consistent simulations of a von Kármán type dynamo in a spherical domain with metallic walls.

10^{-6}

Multiple zonal jets and convective heat transport barriers in a quasi-geostrophic model of planetary cores

, which is continuous at the onset (supercritical bifurcation) and consists of thermal Rossby waves, and (ii) a novel strong branch at lower Ekman numbers, which is discontinuous at the onset. The strong branch becomes subcritical for Ekman numbers of the order of