S. Fauve

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.

Patterns and quasi-patterns in the Faraday experiment

Parametric excitation of surface waves via forced vertical oscillation of a container filled with fluid (the Faraday instability) is investigated experimentally in a small-depth large-aspect-ratio system, with a viscous fluid and with two simultaneous forcing frequencies. The asymptotic pattern observed just above the threshold for the first instability of the flat surface is found to depend strongly on the frequency ratio and the amplitudes and phases of the two sinusoidal components of the driving acceleration. Parallel lines, squares, and hexagons are observed. With viscosity 100 cS, these stable standing-wave patterns do not exhibit strong sidewall effects, and are found in containers of various shapes including an irregular shape. A ‘quasi-pattern’ of twelvefold symmetry, analogous to a two-dimensional quasi-crystal, is observed for some even/odd frequency ratios. Many of the experimental phenomena can be modelled via cubic-order amplitude equations derived from symmetry arguments.

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.

Simple Mechanism for Reversals of Earth's Magnetic Field

We show that a model, recently used to describe all the dynamical regimes of the magnetic field generated by the dynamo effect in the von Kármán sodium experiment, also provides a simple explanation of the reversals of Earths magnetic field, despite strong differences between both systems. The validity of the model relies on the smallness of the magnetic Prandtl number.

Two-parameter study of the routes to chaos

Abstract We study the routes to chaos for a Rayleigh-Benard experiment in mercury, as a function of two parameters, the Rayleigh number ( R ) and the Chandrasekhar number ( Q ). For low Q the main route is a period-doubling cascade of bifurcations occurring at low R . For higher values of Q , two routes are observed, one related to a soft mode instability for moderate R , and a second one related to a three oscillators state, occurring at higher Rayleigh number values.

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.

On the magnetic fields generated by experimental dynamos

We review the results obtained by three successful fluid dynamo experiments and discuss what has been learnt from them about the effect of turbulence on the dynamo threshold and saturation. We then discuss several questions that are still open and propose experiments that could be performed to answer some of them.

Effect of magnetic boundary conditions on the dynamo threshold of von Kármán swirling flows

We study the effect of different boundary conditions on the kinematic dynamo threshold of von Karman type swirling flows in a cylindrical geometry. Using an analytical test flow, we model different boundary conditions: insulating walls all over the flow, effect of sodium at rest on the cylinder side boundary, effect of sodium behind the impellers, effect of impellers or side wall made of a high-magnetic-permeability material. We find that using high-magnetic-permeability boundary conditions decreases the dynamo threshold, the minimum being achieved when they are implemented all over the flow.

Capillary wave turbulence on a spherical fluid surface in low gravity

We report the observation of capillary wave turbulence on the surface of a fluid layer in a low-gravity environment. In such conditions, the fluid covers all the internal surface of the spherical container that is submitted to random forcing. The surface wave amplitude displays power law spectrum over two decades in frequency, corresponding to wavelength from millimeters to a few centimeters. This spectrum is found in roughly good agreement with wave turbulence theory. Such a large-scale observation without gravity waves has never been reached during ground experiments. When the forcing is periodic, two-dimensional spherical patterns are observed on the fluid surface such as subharmonic stripes or hexagons with wavelength satisfying the capillary wave dispersion relation.

Viscous and Inertial Convection at Low Prandtl Number: Experimental Study

Rayleigh-Benard convection in mercury is studied in the vicinity of its threshold with a high-resolution experimental system. The Prandtl number of the fluid is varied between 0.02 and 0.04. The experimental evidence of two different stationary convective regimes, called viscous and inertial, is reported. Their dependence on the Prandtl number P is compared with the theoretical predictions in the small Prandtl-number limit.