Louis Marié

Generation of a magnetic field by dynamo action in a turbulent flow of liquid sodium

We report the observation of dynamo action in the von Kármán sodium experiment, i.e., the generation of a magnetic field by a strongly turbulent swirling flow of liquid sodium. Both mean and fluctuating parts of the field are studied. The dynamo threshold corresponds to a magnetic Reynolds number R(m) approximately 30. A mean magnetic field of the order of 40 G is observed 30% above threshold at the flow lateral boundary. The rms fluctuations are larger than the corresponding mean value for two of the components. The scaling of the mean square magnetic field is compared to a prediction previously made for high Reynolds number flows.

Magnetic field reversals in an experimental turbulent dynamo

We report the first experimental observation of reversals of a dynamo field generated in a laboratory experiment based on a turbulent flow of liquid sodium. The magnetic field randomly switches between two symmetric solutions B and -B. We observe a hierarchy of time scales similar to the Earths magnetic field: the duration of the steady phases is widely distributed, but is always much longer than the time needed to switch polarity. In addition to reversals we report excursions. Both coincide with minima of the mechanical power driving the flow. Small changes in the flow driving parameters also reveal a large variety of dynamo regimes.

A hydrodynamic shear instability in stratified disks

We discuss the possibility that astrophysical accretion disks are dynamically unstable to non-axisymmetric distur- bances with characteristic scales much smaller than the vertical scale height. The instability is studied using three methods: one based on the energy integral, which allows the determination of a sufficient condition of stability, one using a WKB approach, which allows the determination of the necessary and sufficient condition for instability and a last one by numerical solution. This linear instability occurs in any inviscid stably stratified differential rotating fluid for rigid, stress-free or periodic boundary conditions, provided the angular velocity Ω decreases outwards with radius r. At not too small stratification, its growth rate is a fraction of Ω. The influence of viscous dissipation and thermal diffusivity on the instability is studied numerically, with emphasis on the case when d ln Ω/ dl nr = −3/2 (Keplerian case). Strong stratification and large diffusivity are found to have a stabilizing effect. The corresponding critical stratification and Reynolds number for the onset of the instability in a typical disk are derived. We propose that the spontaneous generation of these linear modes is the source of turbulence in disks, especially in weakly ionized disks.

Multistability and memory effect in a highly turbulent flow: experimental evidence for a global bifurcation.

We report experimental evidence of a global bifurcation on a highly turbulent von Kármán flow. The mean flow presents multiple solutions: the canonical symmetric solution becomes marginally unstable towards a flow which breaks the basic symmetry of the driving apparatus even at very large Reynolds numbers. The global bifurcation between these states is highly subcritical and the system thus keeps a memory of its history. The transition recalls low-dimension dynamical system transitions and exhibits very peculiar statistics. We discuss the role of turbulence in two ways: the multiplicity of hydrodynamical solutions and the effect of fluctuations on the nature of transitions.

Magnetohydrodynamics measurements in the von Kármán sodium experiment

We study the magnetic induction in a confined swirling flow of liquid sodium, at integral magnetic Reynolds numbers up to 50. More precisely, we measure in situ the magnetic field induced by the flow motion in the presence of a weak external field. Because of the very small value of the magnetic Prandtl number of all liquid metals, flows with even modest Rm are strongly turbulent. Large mean induction effects are observed over a fluctuating background. As expected from the von Karman flow geometry, the induction is strongly anisotropic. The main contributions are the generation of an azimuthal induced field when the applied field is in the axial direction (an Ω effect) and the generation of axial induced field when the applied field is the transverse direction (as in a large scale α effect). Strong fluctuations of the induced field, due to the flow nonstationarity, occur over time scales slower than the flow forcing frequency. In the spectral domain, they display a f−1 spectral slope. At smaller scales (and larger frequencies) the turbulent fluctuations are in agreement with a Kolmogorov modeling of passive vector dynamics.

Numerical study of homogeneous dynamo based on experimental von Karman type flows

Abstract.A numerical study of the magnetic induction equation has been performed on von Kármán type flows. These flows are generated by two co-axial counter-rotating propellers in cylindrical containers. Such devices are currently used in the von Kármán sodium (VKS) experiment designed to study dynamo action in an unconstrained flow. The mean velocity fields have been measured for different configurations and are introduced in a periodic cylindrical kinematic dynamo code. Depending on the driving configuration, on the poloidal to toroidal flow ratio and on the conductivity of boundaries, some flows are observed to sustain growing magnetic fields for magnetic Reynolds numbers accessible to a sodium experiment. The response of the flow to an external magnetic field has also been studied: The results are in excellent agreement with experimental results in the single propeller case but can differ in the two propellers case.

Galerkin analysis of kinematic dynamos in the von Kármán geometry.

We investigate dynamo action by solving the kinematic dynamo problem for velocity fields of the von Karman type between two coaxial counter-rotating propellers in a cylinder. A Galerkin method is implemented that takes advantage of the symmetries of the flow and their subsequent influence on the nature of the magnetic field at the dynamo threshold. Distinct modes of instability have been identified that differ by their spatial and temporal behaviors. Our calculations give the result that a stationary and antisymmetric mode prevails at the dynamo threshold. We then present a quantitative analysis of the results based on the parametric study of four interaction coefficients obtained by reduction of our initially large eigenvalue problem. We propose these coefficients to measure the relative importance of the different mechanisms at play in the von Karman kinematic dynamo.

Evidence for Forcing-Dependent Steady States in a Turbulent Swirling Flow

We study the influence of the forcing on the steady turbulent states of a von Kármán swirling flow, at constant impeller speed, or at constant torque. We find that the different forcing conditions change the nature of the stability of the steady states and reveal dynamical regimes that bear similarities with low-dimensional systems. We suggest that this forcing dependence may be an outof-equilibrium analogue of the ensemble inequivalence observed in long-range interacting statistical systems, and that it may be applicable to other turbulent systems.

A stochastic model of torques in von Karman swirling flow

Abstract.A stochastic model is derived to predict the turbulent torque produced by a swirling flow. It is a simple Langevin process, with a colored noise. Using the unified colored noise approximation, we derive analytically the PDF of the fluctuations of injected power in two forcing regimes: constant angular velocity or constant applied torque. In the limit of small velocity fluctuations and vanishing inertia, we predict that the injected power fluctuates twice less in the case of constant torque than in the case of constant angular velocity forcing. The model is further tested against experimental data in a von Karman device filled with water. It is shown to allow for a parameter-free prediction of the PDF of power fluctuations in the case where the forcing is made at constant torque. A physical interpretation of our model is finally given, using a quasi-linear model of turbulence.