Transport of magnetic field by a turbulent flow of liquid sodium

We study the effect of a turbulent flow of liquid sodium generated in the von K\'arm\'an geometry, on the localized field of a magnet placed close to the frontier of the flow. We observe that the field can be transported by the flow on distances larger than its integral length scale. In the most turbulent configurations, the mean value of the field advected at large distance vanishes. However, the rms value of the fluctuations increases linearly with the magnetic Reynolds number. The advected field is strongly intermittent.Comment: 4 pages, 6 figure

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.Comment: 40 pages, 13 figure

Wave-vortex interaction

We present an experimental study on the effect of a electromagneticaly generated vortex flow on parametrically amplified waves at the surface of a fluid. The underlying vortex flow, generated by a periodic Lorentz force, creates spatio-temporal fluctuations that interact nonlinearly with the standing surface waves. We characterize the bifurcation diagram and measure the power spectrum density (PSD) of the local surface wave amplitude. We show that the parametric instability threshold increases with increasing intensity of the vortex flow.Comment: 8 pages, 10 figures, submitted to Phys. Rev.

Existence and stability of singular patterns in a Ginzburg–Landau equation coupled with a mean field

We study singular patterns in a particular system of parabolic partial differential equations which consist of a Ginzburg–Landau equation and a mean field equation. We prove the existence of the three simplest concentrated periodic stationary patterns (single spikes, double spikes, double transition layers) by composing them of more elementary patterns and solving the corresponding consistency conditions. In the case of spike patterns we prove stability for sufficiently large spatial periods by first showing that the eigenvalues do not tend to zero as the period goes to infinity and then passing in the limit to a nonlocal eigenvalue problem which can be studied explicitly. For the two other patterns we show instability by using the variational characterization of eigenvalues

A quasi-elastic regime for vibrated granular gases

Using simple scaling arguments and two-dimensional numerical simulations of a granular gas excited by vibrating one of the container boundaries, we study a double limit of small $1-r$ and large $L$, where $r$ is the restitution coefficient and $L$ the size of the container. We show that if the particle density $n_0$ and $(1-r^2)(n_0 Ld)$ where $d$ is the particle diameter, are kept constant and small enough, the granular temperature, i.e. the mean value of the kinetic energy per particle, $/N$, tends to a constant whereas the mean dissipated power per particle, $/N$, decreases like $1/\sqrt{N}$ when $N$ increases, provided that $(1-r^2)(n_0 Ld)^2 < 1$. The relative fluctuations of $E$, $D$ and the power injected by the moving boundary, $I$, have simple properties in that regime. In addition, the granular temperature can be determined from the fluctuations of the power $I(t)$ injected by the moving boundary.

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 which is submitted to random forcing. The surface wave amplitude displays power-law spectrum over two decades in frequency, corresponding to wavelength from $mm$ to a few $cm$. 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