laboratoire de physique statistique
 
 
laboratoire de physique statistique

Publications

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2016
Optimal Length Scale for a Turbulent Dynamo - Sadek, Mira and Alexakis, Alexandros and Fauve, Stephan
PHYSICAL REVIEW LETTERS 116 (2016) 
LPS


Abstract : We demonstrate that there is an optimal forcing length scale for low Prandtl number dynamo flows that can significantly reduce the required energy injection rate. The investigation is based on simulations of the induction equation in a periodic box of size 2 pi L. The flows considered are the laminar and turbulent ABC flows forced at different forcing wave numbers k(f), where the turbulent case is simulated using a subgrid turbulence model. At the smallest allowed forcing wave number k(f) = k(min) = 1/L the laminar critical magnetic Reynolds number Rm(c)(lam) is more than an order of magnitude smaller than the turbulent critical magnetic Reynolds number Rm(c)(turb) due to the hindering effect of turbulent fluctuations. We show that this hindering effect is almost suppressed when the forcing wave number k(f) is increased above an optimum wave number kfL similar or equal to 4 for which Rm(c)(turb) is minimum. At this optimal wave number, Rm(c)(turb) is smaller by more than a factor of 10 than the case forced in k(f) = 1. This leads to a reduction of the energy injection rate by 3 orders of magnitude when compared to the case where the system is forced at the largest scales and thus provides a new strategy for the design of a fully turbulent experimental dynamo.
Instability in electromagnetically driven flows. I - Gissinger, Christophe and Imazio, Paola Rodriguez and Fauve, Stephan
PHYSICS OF FLUIDS 28 (2016) 
LPS


Abstract : The magnetohydrodynamic flow driven by a travelling magnetic field in an annular channel is investigated numerically. For sufficiently large magnetic Reynolds number Rm, or if a large enough pressure gradient is externally applied, the system undergoes an instability in which the flow rate in the channel dramatically drops from synchronism with the wave to much smaller velocities. This transition takes the form of a saddle-node bifurcation for the time-averaged quantities. In this first paper, we characterize the bifurcation and study the stability of the flow as a function of several parameters. We show that the bifurcation of the flow involves a bistability between Poiseuille-like and Hartman-like regimes and relies on magnetic flux expulsion. Based on this observation, new predictions are made for the occurrence of this stalling instability. (C) 2016 AIP Publishing LLC.
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) 
LPS


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
Statistical theory of reversals in two-dimensional confined turbulent flows - Shukla, Vishwanath and Fauve, Stephan and Brachet, Marc
PHYSICAL REVIEW E 94 (2016) 
LPS


Abstract : It is shown that the truncated Euler equation (TEE), i.e., a finite set of ordinary differential equations for the amplitude of the large-scale modes, can correctly describe the complex transitional dynamics that occur within the turbulent regime of a confined two-dimensional flow obeying Navier-Stokes equation (NSE) with bottom friction and a spatially periodic forcing. The random reversals of the NSE large-scale circulation on the turbulent background involve bifurcations of the probability distribution function of the large-scale circulation. We demonstrate that these NSE bifurcations are described by the related TEE microcanonical distribution which displays transitions from Gaussian to bimodal and broken ergodicity. A minimal 13-mode model reproduces these results.
 
2015
Dynamics of reversals and condensates in two-dimensional Kolmogorov flows - Mishra, Pankaj Kumar and Herault, Johann and Fauve, Stephan and Verma, Mahendra K.
PHYSICAL REVIEW E 91 (2015) 
LPS


Abstract : We present numerical simulations of the different two-dimensional flow regimes generated by a constant spatially periodic forcing balanced by viscous dissipation and large-scale drag with a dimensionless damping rate 1/Rh. The linear response to the forcing is a 6 x 6 square array of counterrotating vortices, which is stable when the Reynolds number Re or Rh are small. After identifying the sequence of bifurcations that lead to a spatially and temporally chaotic regime of the flow when Re and Rh are increased, we study the transitions between the different turbulent regimes observed for large Re by varying Rh. A large-scale circulation at the box size (the condensate state) is the dominant mode in the limit of vanishing large-scale drag (Rh large). When Rh is decreased, the condensate becomes unstable and a regime with random reversals between two large-scale circulations of opposite signs is generated. It involves a bimodal probability density function of the large-scale velocity that continuously bifurcates to a Gaussian distribution when Rh is decreased further.
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
Statistical Equilibria of Large Scales in Dissipative Hydrodynamic Turbulence - Dallas, V. and Fauve, S. and Alexakis, A.
PHYSICAL REVIEW LETTERS 115 (2015) 
LPS


Abstract : We present a numerical study of the statistical properties of three-dimensional dissipative turbulent flows at scales larger than the forcing scale. Our results indicate that the large scale flow can be described to a large degree by the truncated Euler equations with the predictions of the zero flux solutions given by absolute equilibrium theory, both for helical and nonhelical flows. Thus, the functional shape of the large scale spectra can be predicted provided that scales sufficiently larger than the forcing length scale but also sufficiently smaller than the box size are examined. Deviations from the predictions of absolute equilibrium are discussed.
DOI
10
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) 
LPS


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.
DOI
11
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
DOI
12
Dynamo action by turbulence in absolute equilibrium - Prasath, Srinivasa Gopalakrishnan Ganga and Fauve, Stephan and Brachet, Marc
EPL 106 (2014) 
LPS


Abstract : We consider the generation of a large-scale magnetic field by a turbulent flow driven by a small-scale helical forcing in a low magnetic Prandtl number fluid. We provide an estimate of the dynamo threshold that takes into account the presence of large-scale turbulent fluctuations by considering that the scales of the flow that mostly contribute to the dynamo process are roughly in absolute equilibrium. We show that turbulent flows in absolute equilibrium do generate dynamos and we compare their growth rates to their laminar counterparts. Finally, we show that the back reaction of the growing magnetic field modifies the statistical properties of turbulent flow by suppressing its kinetic helicity at large magnetic Reynolds number. Copyright (C) EPLA, 2014
DOI
13
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.
DOI
14
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) 
LPS


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.
 
2013
DOI
15
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) 
LPS


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.
DOI
16
Energy transfers during dynamo reversals - Mishra, Pankaj and Gissinger, Christophe and Dormy, Emmanuel and Fauve, Stephan
EPL 104 (2013) 
LPS


Abstract : Using direct numerical simulations of the equations of magnetohydrodynamics, we study reversals of the magnetic field generated by the flow of an electrically conducting fluid in a sphere. We show that at low magnetic Prandtl numbers, Pm = 0.5, the decrease of magnetic energy, ohmic dissipation and power of the Lorentz force during a reversal is followed by an increase of the power injected by the force driving the flow and an increase of viscous dissipation. Cross correlations show that the power of the Lorentz force is in advance with respect to the other energy flows. We also observe that during a reversal, the maximum of the magnetic energy density migrates from one hemisphere to the other and comes back to its initial position, in agreement with recent experimental observations. For larger magnetic Prandtl numbers (Pm - 1, 2), the magnetic field reversals do not display these trends and strongly differ one from another. Copyright (C) EPLA, 2013
 
2012
DOI
17
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) 
LPS


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
18
Chaotic motors - Laroche, C. and Labbe, R. and Petrelis, F. and Fauve, S.
AMERICAN JOURNAL OF PHYSICS 80113-121 (2012) 
LPS


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.
DOI
19
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
20
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.