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We consider the random deposition of objects of variable width and height over a line. The successive additions of these structures create a random interface. We focus on the regime of heavy tailed distributions of the structure width. When the structure center is chosen at random, the problem is exactly solvable and we prove that the interfaces generically tend towards self-affine random curves. The asymptotic behavior reached after a large number of iterations is universal in the sense that it depends on only three parameters: the shape of the added structure at its maximum, the power-law exponent of the width distribution and the exponent that relates height and width. The parameter space displays several transitions that separate different asymptotic behaviors. In particular for a set of parameters, the interface tends towards a fractional Brownian motion. Our results reveal the existence of a new class of random interfaces which properties appear to be robust. The mechanism that generates correlations at large distance is identified and it explains the appearance of such correlations in several situations of interest such as the physics of earthquakes or the propagation of energy through a diffusive medium., Comment: 5 pages, 7 figures

We investigate the spatio-temporal quantity of coherence for turbulent velocity fluctuations at spatial distances of the order or larger than the integral length scale $l_{0}$. Using controlled laboratory experiments, an exponential decay as a function of distance is observed with a decay rate which depends on the flow properties. The same law is observed in two different flows indicating that it can be a generic property of turbulent flows.

We consider capillary wave turbulence at scales larger than the forcing one. At such scales, our measurements show that the surface waves dynamics is the one of a thermal equilibrium state in which the effective temperature is related to the injected power. We characterize this evolution with a scaling law and report the statistical properties of the large-scale surface elevation depending on this effective temperature.

The Von K{\'a}rm{\'a}n 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 $\\theta$ = (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.

Critical exponents are calculated exactly at the onset of an instability, using asymptotic expansiontechniques. When the unstable mode is subject to multiplicative noise whose spectrum at zero frequency vanishes, we show that the critical behavior can be anomalous, i.e. the mode amplitude X scales with departure from onset \mu as $ ~ \mu^\beta$ with an exponent $\beta$ different from its deterministic value. This behavior is observed in a direct numerical simulation of the dynamo instability and our results provide a possible explanation to recent experimental observations.

We present a new mechanism for oscillatory or random reversals of the magnetic field that occur from a stationary dynamo state. The basic ingredient is the existence of two nearly critical dynamo eigenmodes, a stable and an unstable one, that collide during a saddle-node bifurcation. Above this bifurcation, a finite amplitude limit cycle is generated. In the neighbourhood of the bifurcation, even a small amount of turbulent fluctuations is enough to generate random reversals of the magnetic field. When the two competing eigenmodes have different symmetries, this scenario requires a broken symmetry of the flow that generates the dynamo. This is in good agreement with the observations of the VKS experiment. It can also explain the dynamics of planetary or stellar magnetic fields and can be used to understand reversals of large scale flows that often develop on a turbulent background.

We show that a model, recently used to describe all the dynamical regimes of the magnetic field generated by the dynamo effect in the VKS experiment [1], also provides a simple explanation of the reversals of Earth's magnetic field, despite strong differences between both systems., Comment: update version, with new figures

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 figures

We study the flow response to an externally imposed homogeneous magnetic field in a turbulent swirling flow of liquid sodium -- the VKS2 experiment in which magnetic Reynolds numbers Rm up to 50 are reached. Induction effects are larger than in the former VKS1 experiment. At Rm larger than about 25, the local amplitude of induced field components supersedes that of the applied field, and exhibits non-Gaussian fluctuations. Slow dynamical instationarities and low-frequency bimodal dynamics are observed in the induction, presumably tracing back to large scale fluctuations in the hydrodynamic flow.

We report the observation of dynamo action in the VKS experiment, i.e., the generation of 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 Rm \sim 30. A mean magnetic field of order 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., Comment: 4 pages, 5 figures

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 Earth's 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., Comment: 5 pages, 4 figures

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 figures

We report the experimental observation of the alpha-effect. It consists in the generation of a current parallel to a magnetic field B0 applied to a turbulent swirling flow of liquid sodium. At low magnetic Reynolds number, Rm, we show that the magnitude of the alpha-effect increases like Rm2 and that its sign is determined by the flow helicity. It saturates and then decreases at large Rm, primarily because of the expulsion of the applied field B0 from the bulk of the flow. We show how this expulsion is affected by the flow geometry by varying the relative amplitudes of the azimuthal and axial flows., Comment: 9 pages, 4 figures