86 research outputs found
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 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
- …