laboratoire de physique statistique
 
 
laboratoire de physique statistique

Publications

Rechercher
 
2016
Fluctuations of Electrical Conductivity: A New Source for Astrophysical Magnetic Fields - Petrelis, F. and Alexakis, A. and Gissinger, C.
PHYSICAL REVIEW LETTERS 116 (2016) 
LPS


Abstract : We consider the generation of a magnetic field by the flow of a fluid for which the electrical conductivity is nonuniform. A new amplification mechanism is found which leads to dynamo action for flows much simpler than those considered so far. In particular, the fluctuations of the electrical conductivity provide a way to bypass antidynamo theorems. For astrophysical objects, we show through three-dimensional global numerical simulations that the temperature-driven fluctuations of the electrical conductivity can amplify an otherwise decaying large scale equatorial dipolar field. This effect could play a role for the generation of the unusually tilted magnetic field of the iced giants Neptune and Uranus.
Acoustic Measurement of Surface Wave Damping by a Meniscus - Michel, Guillaume and Petrelis, Francois and Fauve, Stephan
PHYSICAL REVIEW LETTERS 116 (2016) 
LPS


Abstract : We investigate the reflection of gravity-capillary surface waves by a plane vertical barrier. The size of the meniscus is found to strongly affect reflection: the energy of the reflected wave with a pinned contact line is around twice the one corresponding to a fully developed meniscus. To perform these measurements, a new experimental setup similar to an acousto-optic modulator is developed and offers a simple way to measure the amplitude, frequency and direction of propagation of surface waves.
Generation of a mean flow by an internal wave - Semin, B. and Facchini, G. and Petrelis, F. and Fauve, S.
PHYSICS OF FLUIDS 28 (2016) 
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Abstract : We experimentally study the generation of a mean flow by a two-dimensional progressive internal gravity wave. Due to the viscous damping of the wave, a non-vanishing Reynolds stress gradient forces a mean flow. When the forcing amplitude is low, the wave amplitude is proportional to the forcing and the mean flow is quadratic in the forcing. When the forcing amplitude is large, the mean flow decreases the wave amplitude. This feedback saturates both the wave and the mean flow. The profiles of the mean flow and the wave are compared with a one-dimensional analytical model. Decreasing the forcing frequency leads to a wave and a mean flow localized on a smaller height, in agreement with the model. Published by AIP Publishing.
Bifurcations of a large-scale circulation in a quasi-bidimensional turbulent flow - Michel, G. and Herault, J. and Petrelis, F. and Fauve, S.
EPL 115 (2016) 
LPS


Abstract : We report the experimental study of the bifurcations of a large-scale circulation that is formed over a turbulent flow generated by a spatially periodic forcing. After shortly describing how the flow becomes turbulent through a sequence of symmetry-breaking bifurcations, we focus our study on the transitions that occur within the turbulent regime. They are related to changes in the shape of the probability density function (PDF) of the amplitude of the large-scale flow. We discuss the nature of these bifurcations and how to model the shape of the PDF. Copyright (C) EPLA, 2016
 
2015
Experimental observation of 1/f noise in quasi-bidimensional turbulent flows - Herault, J. and Petrelis, F. and Fauve, S.
EPL 111 (2015) 
LPS


Abstract : We report the experimental observation of 1/f(alpha) noise in quasi-bidimensional turbulence of an electromagnetically forced flow. The large-scale velocity U-L exhibits this power-law spectrum with alpha approximate to 0.7 over a range of frequencies smaller than both the characteristic turnover frequency and the damping rate of the flow. By studying the statistical properties of sojourn time in each polarity of U-L, we demonstrate that the 1/f(alpha) noise is generated by a renewal process, defined by a two-state model given by the polarities of the large-scale circulation. The statistical properties of this renewal process are shown to control the value of the exponent alpha. Copyright (C) EPLA, 2015
1/f(alpha) Low Frequency Fluctuations in Turbulent Flows Transitions with Heavy-Tailed Distributed Interevent Durations - Herault, J. and Petrelis, F. and Fauve, S.
JOURNAL OF STATISTICAL PHYSICS 1611379-1389 (2015) 
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Abstract : We report the experimental observation of low frequency fluctuations with a spectrum varying as in three different turbulent flow configurations: the large scale velocity driven by a two-dimensional turbulent flow, the magnetic field generated by a turbulent swirling flow of liquid sodium and the pressure fluctuations due to vorticity filaments in a swirling flow. For these three systems, noise is shown to result from the dynamics of coherent structures that display transitions between a small number of states. The interevent duration is distributed as a power law. The exponent of this power law and the nature of the dynamics (transition between symmetric states or asymmetric ones) select the exponent of the fluctuations.
Drifting patterns as field reversals - Petrelis, F. and Laroche, C. and Gallet, B. and Fauve, S.
EPL 112 (2015) 
LPS


Abstract : One-dimensional patterns generated by the Faraday instability at the surface of a vertically vibrated fluid are investigated when the reflection symmetry in the direction of the pattern is broken. For large symmetry breaking, the stationary instability turns into a Hopf bifurcation at a codimension-2 point. This Hopf bifurcation amounts to a periodic drift of the pattern. Further above the onset of the instability, this drift transition competes with the Eckhaus instability as predicted by the study of a model built upon the Swift-Hohenberg equation. In the presence of noise, the drift becomes random and time series of the pattern amplitude display random reversals (sign changes). We show that these reversals belong to the same class as those observed in a variety of contexts such as magnetic fields generated by dynamo action. Copyright (C) EPLA, 2015
 
2014
Decay rates of magnetic modes below the threshold of a turbulent dynamo - Herault, J. and Petrelis, F. and Fauve, S.
PHYSICAL REVIEW E 89 (2014) 
LPS


Abstract : We measure the decay rates of magnetic field modes in a turbulent flow of liquid sodium below the dynamo threshold. We observe that turbulent fluctuations induce energy transfers between modes with different symmetries (dipolar and quadrupolar). Using symmetry properties, we show how to measure the decay rate of each mode without being restricted to the one with the smallest damping rate. We observe that the respective values of the decay rates of these modes depend on the shape of the propellers driving the flow. Dynamical regimes, including field reversals, are observed only when the modes are both nearly marginal. This is in line with a recently proposed model.
Dynamo efficiency controlled by hydrodynamic bistability - Miralles, Sophie and Herault, Johann and Fauve, Stephan and Gissinger, Christophe and Petrelis, Francois and Daviaud, Francois and Dubrulle, Berengere and Boisson, Jean and Bourgoin, Mickael and Verhille, Gautier and Odier, Philippe and Pinton, Jean-Francois and Plihon, Nicolas
PHYSICAL REVIEW E 89 (2014) 
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Abstract : Hydrodynamic and magnetic behaviors in a modified experimental setup of the von Karman sodium flow-where one disk has been replaced by a propeller-are investigated. When the rotation frequencies of the disk and the propeller are different, we show that the fully turbulent hydrodynamic flow undergoes a global bifurcation between two configurations. The bistability of these flow configurations is associated with the dynamics of the central shear layer. The bistable flows are shown to have different dynamo efficiencies; thus for a given rotation rate of the soft-iron disk, two distinct magnetic behaviors are observed depending on the flow configuration. The hydrodynamic transition controls the magnetic field behavior, and bifurcations between high and low magnetic field branches are investigated.
DOI
10
Optimum reduction of the dynamo threshold by a ferromagnetic layer located the flow - Herault, J. and Petrelis, F.
PHYSICAL REVIEW E 90 (2014) 
LPS


Abstract : We consider a fluid dynamo model generated by the flow on both sides of a moving layer. The magnetic permeability of the layer is larger than that of the flow. We show that there exists an optimum value of magnetic permeability for which the critical magnetic Reynolds number for dynamo onset is smaller than for a nonmagnetic material and also smaller than for a layer of infinite magnetic permeability. We present a mechanism that provides an explanation for recent experimental results. A similar effect occurs when the electrical conductivity of the layer is large.
 
2013
DOI
11
Spatial variations of magnetic permeability as a source of dynamo action - Gallet, B. and Petrelis, F. and Fauve, S.
JOURNAL OF FLUID MECHANICS 727161-190 (2013) 
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Abstract : We investigate dynamo action for a parallel flow of an electrically conducting fluid located over a boundary with spatially varying magnetic permeability. We first compute the dynamo threshold numerically. Then we perform an asymptotic expansion in the limit of small permeability modulation, which gives accurate results even for moderate modulation. We present in detail the mechanism at work for this dynamo It is an interplay between shear (an omega-effect) and a new conversion mechanism that originates from the non-uniform magnetic boundary. We illustrate how a similar mechanism leads to dynamo action in the case of spatially modulated electrical conductivity, a problem studied by Busse \& Wicht (Geophys. Astrophys. Fluid Dyn., vol. 64, 1992, pp. 135-144). Finally, we discuss the relevance of this effect to experimental dynamos and present ways to increase the dynamo efficiency and reduce the instability threshold.
 
2012
DOI
12
Reversals of a large-scale field generated over a turbulent background - Gallet, B. and Herault, J. and Laroche, C. and Petrelis, F. and Fauve, S.
GEOPHYSICAL AND ASTROPHYSICAL FLUID DYNAMICS 106468-492 (2012) 
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Abstract : We present a study of several systems in which a large-scale field is generated over a turbulent background. These large-scale fields break a symmetry of the forcing by selecting a direction. Under certain conditions, the large-scale field displays reversals so that the symmetry of the forcing is recovered statistically. We present examples of such dynamics in the context of the dynamo instability, of two-dimensional turbulent Kolmogorov flows and of turbulent Rayleigh-Benard convection. In these systems reversals occur respectively for the dynamo magnetic field, for the large-scale circulation generated by a periodic forcing in space and for the large-scale roll generated by turbulent thermal convection. We compare the mechanisms involved and show that their properties depend on some symmetries of the system and on the way they are broken.
DOI
13
Anomalous Exponents at the Onset of an Instability - Petrelis, F. and Alexakis, A.
PHYSICAL REVIEW LETTERS 108 (2012) 
LPS


Abstract : Critical exponents are calculated exactly at the onset of an instability, by using asymptotic expansion techniques. 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 < X > proportional to 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 for recent experimental observations.
DOI
14
Chaotic motors - Laroche, C. and Labbe, R. and Petrelis, F. and Fauve, S.
AMERICAN JOURNAL OF PHYSICS 80113-121 (2012) 
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Abstract : We show that electric motors and dynamos can be used to illustrate most elementary instabilities or bifurcations discussed in courses on nonlinear oscillators and dynamical systems. These examples are easier to understand and display a richer behavior than the ones commonly used from mechanics, electronics, hydrodynamics, lasers, chemical reactions, and population dynamics. In particular, an electric motor driven by a dynamo can display stationary, Hopf, and codimension-two bifurcations by tuning the driving speed of the dynamo and the electric current in the stator of the electric motor. When the dynamo is driven at constant torque instead of constant rotation rate, chaotic reversals of the generated current and of the angular rotation of the motor are observed. Simple deterministic models are presented which capture the observed dynamical regimes. (C) 2012 American Association of Physics Teachers.
15
When north heads south - Petrelis, Francois and Valet, Jean-Pierre and Besse, Jean
PHYSICS WORLD 2551-55 (2012) 
LPS
DOI
16
Dynamo action due to spatially dependent magnetic permeability - Gallet, B. and Petrelis, F. and Fauve, S.
EPL 97 (2012) 
LPS


Abstract : We show that a simple flow of an electrically conducting fluid along a boundary with variable magnetic permeability can generate a magnetic field. An analytic study in the limit of weak permeability modulation allows to understand the mechanism of this dynamo and predicts scaling laws for the threshold. We discuss the possible contribution of this mechanism to the dynamo observed in the von Karman sodium experiment and we propose two flow configurations that could lead to the experimental observation of this new type of dynamo. Copyright (C) EPLA, 2012
DOI
17
Experimental Observation of Spatially Localized Dynamo Magnetic Fields - Gallet, B. and Aumaitre, S. and Boisson, J. and Daviaud, F. and Dubrulle, B. and Bonnefoy, N. and Bourgoin, M. and Odier, Ph. and Pinton, J. -F. and Plihon, N. and Verhille, G. and Fauve, S. and Petrelis, F.
PHYSICAL REVIEW LETTERS 108 (2012) 
LPS


Abstract : We report the first experimental observation of a spatially localized dynamo magnetic field, a common feature of astrophysical dynamos and convective dynamo simulations. When the two propellers of the von Karman sodium experiment are driven at frequencies that differ by 15\%, the mean magnetic field's energy measured close to the slower disk is nearly 10 times larger than the one close to the faster one. This strong localization of the magnetic field when a symmetry of the forcing is broken is in good agreement with a prediction based on the interaction between a dipolar and a quadrupolar magnetic mode.
DOI
18
Critical Exponents in Zero Dimensions - Alexakis, A. and Petrelis, F.
JOURNAL OF STATISTICAL PHYSICS 149738-753 (2012) 
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Abstract : 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.
 
2011
DOI
19
Plate tectonics may control geomagnetic reversal frequency - Petrelis, F. and Besse, J. and Valet, J. -P.
GEOPHYSICAL RESEARCH LETTERS 38 (2011) 
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Abstract : The discovery of the reversals of Earth's magnetic field and the description of plate tectonics are two of the main breakthroughs in geophysics in the 20th century. We claim that these two phenomena are correlated and that plate tectonics controls long-term changes in geomagnetic reversal frequency. More precisely, geological intervals characterized by an asymmetrical distribution of the continents with respect to the equator are followed by intervals of high reversal frequency. We speculate that the distribution and symmetry of mantle structures driving continental motions at the surface influence the equatorial symmetry of the flow within the core and thus change the coupling between the dipolar and quadrupolar modes which controls the occurrence of reversals. Citation: Petrelis, F., J. Besse, and J.-P. Valet (2011), Plate tectonics may control geomagnetic reversal frequency, Geophys. Res. Lett., 38, L19303, doi:10.1029/2011GL048784.
 
2010
DOI
20
Mechanisms for magnetic field reversals - Petrelis, F. and Fauve, S.
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES 3681595-1605 (2010) 
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Abstract : We present a review of the different models that have been proposed to explain reversals of the magnetic field generated by a turbulent flow of an electrically conducting fluid (fluid dynamos). We then describe a simple mechanism that explains several features observed in palaeomagnetic records of the Earth's magnetic field, in numerical simulations and in a recent dynamo experiment. A similar model can also be used to understand reversals of large-scale flows that often develop on a turbulent background.