Sébastien Aumaître

The von Karman Sodium experiment: Turbulent dynamical dynamos

The von Karman Sodium (VKS) experiment studies dynamo action in the flow generated inside a cylinder filled with liquid sodium by the rotation of coaxial impellers (the von Karman geometry). We first report observations related to the self-generation of a stationary dynamo when the flow forcing is R-pi-symmetric, i.e., when the impellers rotate in opposite directions at equal angular velocities. The bifurcation is found to be supercritical with a neutral mode whose geometry is predominantly axisymmetric. We then report the different dynamical dynamo regimes observed when the flow forcing is not symmetric, including magnetic field reversals. We finally show that these dynamics display characteristic features of low dimensional dynamical systems despite the high degree of turbulence in the flow.

Low-frequency noise controls on-off intermittency of bifurcating systems.

A bifurcating system subject to multiplicative noise can display on-off intermittency. Using a canonical example, we investigate the extreme sensitivity of the intermittent behavior to the nature of the noise. Through a perturbative expansion and numerical studies of the probability density function of the unstable mode, we show that intermittency is controlled by the ratio between the departure from onset and the value of the noise spectrum at zero frequency. Reducing the noise spectrum at zero frequency shrinks the intermittency regime drastically. This effect also modifies the distribution of the duration that the system spends in the off phase. Mechanisms and applications to more complex bifurcating systems are discussed.

Dynamo regimes and transitions in the VKS experiment

Abstract. The Von Kármán Sodium experiment yields a variety of dynamo regimes, when asymmetry is imparted to the flow by rotating impellers at different speed F1 and F2. We show that as the intensity of forcing, measured as F1+F2, is increased, the transition to a self-sustained magnetic field is always observed via a supercritical bifurcation to a stationary state. For some values of the asymmetry parameter θ = (F1–F2)/(F1+F2), time dependent dynamo regimes develop. They are observed either when the forcing is increased for a given value of asymmetry, or when the amount of asymmetry is varied at sufficiently high forcing. Two qualitatively different transitions between oscillatory and stationary regimes are reported, involving or not a strong divergence of the period of oscillations. These transitions can be interpreted using a low dimensional model based on the interactions of two dynamo modes.

Bistability between a stationary and an oscillatory dynamo in a turbulent flow of liquid sodium

We report the first experimental observation of a bistable dynamo regime. A turbulent flow of liquid sodium is generated between two disks in the von Karman geometry (VKS experiment). When one disk is kept at rest, bistability is observed between a stationary and an oscillatory magnetic field. The stationary and oscillatory branches occur in the vicinity of a codimension-two bifurcation that results from the coupling between two modes of magnetic field. We present an experimental study of the two regimes and study in detail the region of bistability that we understand in terms of dynamical system theory. Despite the very turbulent nature of the flow, the bifurcations of the magnetic field are correctly described by a low-dimensional model. In addition, the different regimes are robust; i.e. turbulent fluctuations do not drive any transition between the oscillatory and stationary states in the region of bistability.

Fluctuations of energy flux in wave turbulence.

We report that the power driving gravity and capillary wave turbulence in a statistically stationary regime displays fluctuations much stronger than its mean value. We show that its probability density function (PDF) has a most probable value close to zero and involves two asymmetric roughly exponential tails. We understand the qualitative features of the PDF using a simple Langevin-type model.

Observation of resonant interactions among surface gravity waves

We experimentally study resonant interactions of oblique surface gravity waves in a large basin. Our results strongly extend previous experimental results performed mainly for perpendicular or collinear wave trains. We generate two oblique waves crossing at an acute angle, while we control their frequency ratio, steepnesses and directions. These mother waves mutually interact and give birth to a resonant wave whose properties (growth rate, resonant response curve and phase locking) are fully characterized. All our experimental results are found in good quantitative agreement with four-wave interaction theory with no fitting parameter. Off-resonance experiments are also reported and the relevant theoretical analysis is conducted and validated.

Symmetry and couplings in stationary Von Kármán sodium dynamos

We study different types of stationary dynamos observed in the Von Karman sodium (VKS) experiment when varying the electromagnetic boundary conditions on (and in) the impellers. The flow is driven with two impellers made of soft iron (Monchaux et al 2007 Phys Rev. Lett. 98 044502) or using one soft-iron impeller and one stainless steel impeller. The magnetic field is mapped using 40 three-dimensional probes distributed within the flow and its surroundings. Symmetry and coupling properties are then retrieved from direct probe measurements and/or from the field structure as reconstructed using the inversion procedure described by Boisson and Dubrulle (2011 New J. Phys. 13 023037). Several salient results are obtained: (i) dynamo action is not achieved unless at least one iron impeller is rotating, at a frequency larger than 15 Hz; (ii) the resulting dynamo is a dipolar, mostly axisymmetric structure; and (iii) the self-sustained magnetic field properties depend on the sodium flow structure between the two impellers. We propose to interpret the stationary dynamos generation as the (constructive or destructive) superposition of two one-impeller fluid dynamos generated close to the soft-iron impellers, nonlinearly coupled through the turbulent flow, as suggested by Verhille et al (2010 New J. Phys. 12 033006). The normal form equation describing this coupling is similar to the one obtained in a theoretical model (Petrelis et al 2009 Phys. Rev. Lett. 102 144503).

Comparing flow thresholds and dynamics for oscillating and inclined granular layers.

The onset and dynamics of flow in shallow horizontally oscillating granular layers are studied as a function of the depth of the layer and imposed acceleration. Measurements of the flow velocity made from the top and side are presented in the frame of reference of the container. As is also found for avalanches of inclined layers, the thresholds for starting and stopping of flow are slightly different. The variation with depth of the starting acceleration Gamma{start} for the oscillating layer is similar to the corresponding variation of the tangent of the starting angle tan(theta{start}) for avalanches in the same container at low frequencies, but deviates as the frequency is increased. However, the threshold behavior depends significantly on the measurement protocol. Just above Gamma{start} , the motion decays with time as the material reorganizes over a minute or so, causing the apparent threshold to increase. Furthermore, the rms velocity as a function of acceleration rises more sharply above the starting threshold if the first minute or so of excitation is discarded. Once excited, the rheology of the material is found to vary in time during the cycle in surprising ways. If the maximum inertial force (proportional to the container acceleration amplitude) is slightly higher than that required to produce flow, the flow velocity grows as soon as the inertial force exceeds zero in each cycle, but jamming occurs long before the inertial force returns to zero. At higher Gamma , the motion is fluidlike over the entire cycle. However, the fraction of the cycle during which the layer is mobile is typically far higher than what one would predict from static considerations or the behavior of the inclined layer. Finally, we consider the flow profiles as a function of both the transverse distance across the cell at the free surface and also as a function of the vertical coordinate in the boundary layer near the sidewall. These profiles have time-dependent shapes and are therefore significantly different from profiles previously measured for avalanche flows.

Noise-induced bifurcations, multiscaling and on?off intermittency

We present recent results on noise-induced transitions in a nonlinear oscillator with randomly modulated frequency. The presence of stochastic perturbations drastically alters the dynamical behaviour of the oscillator: noise can wash out a global attractor but can also have a constructive role by stabilizing an unstable fixed point. The random oscillator displays a rich phenomenology but remains elementary enough to allow for exact calculations: this system is thus a useful paradigm for the study of noise-induced bifurcations and is an ideal testing ground for various mathematical techniques. We show that the phase is determined by the sign of the Lyapunov exponent (which can be calculated non-perturbatively for white noise), and we derive the full phase diagram of the system. We also investigate the effect of time correlations of the noise on the phase diagram and show that a smooth random perturbation is less efficient than white noise. We study the critical behaviour near the transition and explain why noise-induced transitions often exhibit intermittency and multiscaling: these effects do not depend on the amplitude of the noise but rather on its power spectrum. By increasing or filtering out the low frequencies of the noise, intermittency and multiscaling can be enhanced or eliminated.

Travelling waves in a cylindrical magnetohydrodynamically forced flow

We present an experimental study of a liquid metal flow electromagnetically forced in a large aspect ratio coaxial cylindrical geometry. An azimuthal Lorentz force is applied on the liquid metal gap, through a radial current and an axial magnetic field. Using ultrasonic velocity measurements, we focus on the effect of these two parameters on the flow properties. We show that, depending on the strength of the magnetic field and not only on the applied Lorentz force, different dynamical states exist. We first observe a stationary structure at low forcing. Then, two other regimes of different travelling waves are exhibited at higher forcing. We characterize them by their different frequencies and speeds. Higher magnetic fields clearly promote the faster waves. Connections with other magnetohydrodynamics instabilities are discussed.