Stochastic Resonance in a simple model of magnetic reversals

We discuss the effect of stochastic resonance in a simple model of magnetic reversals. The model exhibits statistically stationary solutions and bimodal distribution of the large scale magnetic field. We observe a non trivial amplification of stochastic resonance induced by turbulent fluctuations, i.e. the amplitude of the external periodic perturbation needed for stochastic resonance to occur is much smaller than the one estimated by the equilibrium probability distribution of the unperturbed system. We argue that similar amplifications can be observed in many physical systems where turbulent fluctuations are needed to maintain large scale equilibria.Comment: 6 page

Critical exponents in zero dimensions

In the vicinity of the onset of an instability, we investigate the effect of colored multiplicative noise on the scaling of the moments of the unstable mode amplitude. We introduce a family of zero dimensional models for which we can calculate the exact value of the critical exponents $\beta_m$ for all the moments. The results are obtained through asymptotic expansions that use the distance to onset as a small parameter. The examined family displays a variety of behaviors of the critical exponents that includes anomalous exponents: exponents that differ from the deterministic (mean-field) prediction, and multiscaling: non-linear dependence of the exponents on the order of the moment

On the properties of steady states in turbulent axisymmetric flows

We experimentally study the properties of mean and most probable velocity fields in a turbulent von K\'arm\'an flow. These fields are found to be described by two families of functions, as predicted by a recent statistical mechanics study of 3D axisymmetric flows. We show that these functions depend on the viscosity and on the forcing. Furthermore, when the Reynolds number is increased, we exhibit a tendency for Beltramization of the flow, i.e. a velocity-vorticity alignment. This result provides a first experimental evidence of nonlinearity depletion in non-homogeneous non-isotropic turbulent flow.Comment: latex prl-stationary-051215arxiv.tex, 9 files, 6 figures, 4 pages (http://www-drecam.cea.fr/spec/articles/S06/008/

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 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 figure

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

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

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 figure

Statistical mechanics of Beltrami flows in axisymmetric geometry: Equilibria and bifurcations

We characterize the thermodynamical equilibrium states of axisymmetric Euler-Beltrami flows. They have the form of coherent structures presenting one or several cells. We find the relevant control parameters and derive the corresponding equations of state. We prove the coexistence of several equilibrium states for a given value of the control parameter like in 2D turbulence [Chavanis and Sommeria, J. Fluid Mech. 314, 267 (1996)]. We explore the stability of these equilibrium states and show that all states are saddle points of entropy and can, in principle, be destabilized by a perturbation with a larger wavenumber, resulting in a structure at the smallest available scale. This mechanism is therefore reminiscent of the 3D Richardson energy cascade towards smaller and smaller scales. Therefore, our system is truly intermediate between 2D turbulence (coherent structures) and 3D turbulence (energy cascade). We further explore numerically the robustness of the equilibrium states with respect to random perturbations using a relaxation algorithm in both canonical and microcanonical ensembles. We show that saddle points of entropy can be very robust and therefore play a role in the dynamics. We evidence differences in the robustness of the solutions in the canonical and microcanonical ensembles. A scenario of bifurcation between two different equilibria (with one or two cells) is proposed and discussed in connection with a recent observation of a turbulent bifurcation in a von Karman experiment [Ravelet et al., Phys. Rev. Lett. 93, 164501 (2004)].Comment: 25 pages; 16 figure