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We present experimental evidence of a thermoelectric effect at the interface between two liquid metals. Using superimposed layers of mercury and gallium in a cylindrical vessel operating at room temperature, we provide a direct measurement of the electric current generated by the presence of a thermal gradient along a liquid-liquid interface. At the interface between two liquids, temperature gradients induced by thermal convection lead to a complex geometry of electric currents, ultimately generating current densities near boundaries that are significantly higher than those observed in conventional solid-state thermoelectricity. When a magnetic field is applied to the experiment, an azimuthal shear flow, exhibiting opposite circulation in each layer, is generated. Depending on the value of the magnetic field, two different flow regimes are identified, in good agreement with a model based on the spatial distribution of thermoelectric currents, which has no equivalent in solid systems. Finally, we discuss various applications of this effect, such as the efficiency of liquid metal batteries., Competing Interests: Competing interests statement:The authors declare no competing interest.

In his seminal work on turbulence, Kolmogorov made use of the stationary hypothesis to determine the power density spectrum of the velocity field in turbulent flows. However, to our knowledge, the constraints that stationary processes impose on the fluctuations of the energy flux have never been used in the context of turbulence. Here, we recall that the power density spectra of the fluctuations of the injected power, the dissipated power, and the energy flux have to converge to a common value at vanishing frequency. Hence, we show that the intermittent Gledzer-Ohkitani-Yamada (GOY) shell model fulfills these constraints. We argue that they can be related to intermittency. Indeed, we find that the constraint on the fluctuations of the energy flux implies a relation between the scaling exponents that characterize intermittency, which is verified by the GOY shell model and in agreement with the She-Leveque formula. It also fixes the intermittency parameter of the log-normal model at a realistic value. The relevance of these results for real turbulence is drawn in the concluding remarks.

We report a laboratory study of the transport of angular momentum by a turbulent flow of an electrically conducting fluid confined in a thin disk. When the electromagnetic force applied to the liquid metal is large enough, the corresponding volume injection of angular momentum produces a turbulent flow characterized by a time-averaged Keplerian rotation rate Ω[over ¯]∼r^{-3/2}. Two contributions to the local angular momentum transport are identified: one from the poloidal recirculation induced by the presence of boundaries and the other from turbulent fluctuations in the bulk. The latter produces efficient angular momentum transport independent of the molecular viscosity of the fluid and leads to Kraichnan's prediction Nu_{Ω}∝sqrt[Ta]. In this so-called ultimate regime, the experiment, therefore, provides a configuration analogous to accretion disks, allowing the prediction of accretion rates induced by Keplerian turbulence.

We investigate the spatiotemporal 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 that 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.

A shear flow of liquid metal (Galinstan) is driven in an annular channel by counter-rotating traveling magnetic fields imposed at the end caps. When the traveling velocities are large, the flow is turbulent and its azimuthal component displays random reversals. Power spectra of the velocity field exhibit a 1/f^{α} power law on several decades and are related to power-law probability distributions P(τ)∼τ^{-β} of the waiting times between successive reversals. This 1/f type spectrum is observed only when the Reynolds number is large enough. In addition, the exponents α and β are controlled by the symmetry of the system; a continuous transition between two different types of Flicker noise is observed as the equatorial symmetry of the flow is broken, in agreement with theoretical predictions.

The quasibiennial oscillation (QBO) is the nearly periodic reversal of the large scale flow generated by internal waves in the equatorial stratosphere. Using a laboratory model experiment, we study the instability that generates the QBO and investigate its nonlinear regime. We report the first quantitative measurements of the nonlinearly saturated velocity of the flow. We show that the QBO is generated by a bifurcation that is either supercritical or subcritical depending on the dominant dissipative process. This is confirmed by a nonlinear analysis in the vicinity of the instability threshold.

A new experimental facility has been designed and constructed to study driven granular media in a low-gravity environment. This versatile instrument, fully automatized, with a modular design based on several interchangeable experimental cells, allows us to investigate research topics ranging from dilute to dense regimes of granular media such as granular gas, segregation, convection, sound propagation, jamming, and rheology-all without the disturbance by gravitational stresses active on Earth. Here, we present the main parameters, protocols, and performance characteristics of the instrument. The current scientific objectives are then briefly described and, as a proof of concept, some first selected results obtained in low gravity during parabolic flight campaigns are presented.

We investigate 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.

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.

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.

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 2πL. 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 k_{f}L≃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.

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.

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 6×6 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.

Hydrodynamic and magnetic behaviors in a modified experimental setup of the von Kármán 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.

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.

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 Kármán 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., (© 2012 American Physical Society)

We present a numerical study of the magnetic field generated by the Taylor-Green vortex. We show that periodic boundary conditions can be used to mimic realistic boundary conditions by prescribing the symmetries of the velocity and magnetic fields. This gives insight into some problems of central interest for dynamos: the possible effect of velocity fluctuations on the dynamo threshold, and the role of boundary conditions on the threshold and on the geometry of the magnetic field generated by dynamo action. In particular, we show that an axial dipolar dynamo similar to the one observed in a recent experiment can be obtained with an appropriate choice of the symmetries of the magnetic field. The nonlinear saturation is studied and a simple model explaining the magnetic Prandtl number dependence of the super- and subcritical nature of the dynamo transition is given.

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.

We present an experimental study of the effect of an electromagnetically generated vortex flow on parametrically amplified waves at the surface of a vertically vibrated fluid layer. The underlying vortex flow, generated by a periodic Lorentz force, creates spatiotemporal fluctuations that nonlinearly interact with the standing surface waves. We measure the power spectral density of the surface wave amplitude and we characterize the bifurcation diagram by recording the subharmonic response of the surface to the external vibration. We show that the parametric instability is delayed in the presence of spatiotemporal fluctuations due to the vortex flow. In addition, the dependence of the amplitude of the subharmonic response on the distance to the instability threshold is modified. This shows that the nonlinear saturation mechanism of the waves is modified by the vortex flow.

We show that a model, recently used to describe all the dynamical regimes of the magnetic field generated by the dynamo effect in the von Kármán sodium experiment, also provides a simple explanation of the reversals of Earth's magnetic field, despite strong differences between both systems. The validity of the model relies on the smallness of the magnetic Prandtl number.

We present a numerical study of the magnetic field generated by an axisymmetrically forced flow in a spherical domain. We show that, even in the absence of nonaxisymmetric velocity fluctuations, a mean magnetic field with a dominant axisymmetric dipolar component can be generated via a secondary bifurcation from an equatorial dipole. We understand the dynamical behaviors that result from the interaction of equatorial and axial dipolar modes using simple model equations for their amplitudes derived from symmetry arguments.

We report the observation of several dynamical regimes of the magnetic field generated by a turbulent flow of liquid sodium (VKS experiment). Stationary dynamos, transitions to relaxation cycles or to intermittent bursts, and random field reversals occur in a fairly small range of parameters. Large scale dynamics of the magnetic field result from the interactions of a few modes. The low dimensional nature of these dynamics is not smeared out by the very strong turbulent fluctuations of the flow.

The magnetic field of planets or stars is generated by the motion of a conducting fluid through a dynamo instability. The saturation of the magnetic field occurs through the reaction of the Lorentz force on the flow. In relation to this phenomenon, we study the effect of a magnetic field on a turbulent flow of liquid gallium. The measurement of electric potential differences provides a signal related to the local velocity fluctuations. We observe a reduction of velocity fluctuations at all frequencies in the spectrum when the magnetic field is increased.

We report that the power driving gravity and capillary wave turbulence in a statistically stationary regime displays fluctuations much stronger than its mean value. We show that its probability density function (PDF) has a most probable value close to zero and involves two asymmetric roughly exponential tails. We understand the qualitative features of the PDF using a simple Langevin-type model.

We report the observation of intermittency in gravity-capillary wave turbulence on the surface of mercury. We measure the temporal fluctuations of surface wave amplitude at a given location. We show that the shape of the probability density function of the local slope increments of the surface waves strongly changes across the time scales. The related structure functions and the flatness are found to be power laws of the time scale on more than one decade. The exponents of these power laws increase nonlinearly with the order of the structure function. All these observations show the intermittent nature of the increments of the local slope in wave turbulence. We discuss the possible origin of this intermittency.

We report the observation of the crossover between gravity and capillary wave turbulence on the surface of mercury. The probability density functions of the turbulent wave height are found to be asymmetric and thus non-Gaussian. The surface wave height displays power-law spectra in both regimes. In the capillary region, the exponent is in fair agreement with weak turbulence theory. In the gravity region, it depends on the forcing parameters. This can be related to the finite size of the container. In addition, the scaling of those spectra with the mean energy flux is found in disagreement with weak turbulence theory for both regimes.

We report the observation of dynamo action in the von Kármán sodium experiment, i.e., the generation of a 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 R(m) approximately 30. A mean magnetic field of the order of 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.

We study the effect of a turbulent flow of liquid sodium generated in the von Kármán 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.

Recent experimental study of a granular gas fluidized by vibrations in a low gravity environment has reported that the collision frequency nu(rho) of the particles with the container boundary scales roughly like N(alpha) with alpha=0.6 +/- 0.1, where N is the number of particles. Using numerical simulations, we show that this scaling is observed on a wide range of N, both for nu(rho) and for the particle-particle collision frequency nu(c). Simple scaling arguments show that this behavior is related to the energy flux in the granular gas, from injection by the moving boundary to dissipation by inelastic collisions. We predict in the dilute limit that the collision frequencies scale such as (sqrt)N are in fair agreement with experimental measurements.

We report an experimental study on the effect of an external phase noise on the parametric amplification of surface waves. We observe that both the instability growth rate and the wave amplitude above the instability onset are decreased in the presence of noise. We show that all the results can be understood with a deterministic amplitude equation for the wave in which the effect of noise is just to change the forcing term. All the data for the growth rate (respectively the wave amplitude), obtained for different forcing amplitudes and different intensities of the noise, can be collapsed on a single curve using this renormalized forcing in the presence of noise.

We report an experimental study of the backscattering of a sound wave of frequency f by a surface vibrating harmonically at frequency F (F << f) and amplitude A in the regime where the Doppler effect overcomes bulk nonlinear effects. When the duration to of the analyzed time series of the scattered wave is small compared to the vibration period, the power spectrum of the backscattered wave is proportional to the probability density function of the scatterer velocity, which presents two peaks shifted from f by roughly 2fAomega/c (omega = 2piF). On the contrary, when t0 >> F(-1), sidebands at frequencies f +/- nF (n integer) appear in the power spectrum, which are due to the phase modulation of the backscattered wave induced by its reflection on a moving boundary. We use the backscattered power spectrum to validate the phase modulation theory of the Doppler effect in the latter case for 2kA << 1 and 2kA approximately > 1 (k = 2pif/c, where c is the wave velocity) and we test the validity of an acoustic nonintrusive estimator of A as a function of power spectrum bandwidth and of A itself.

We report the observation of two types of Sommerfeld precursors (or forerunners) on the surface of a layer of mercury. When the fluid depth increases, we observe a transition between these two precursor surface waves in good agreement with the predictions of asymptotic analysis. At depths thin enough compared to the capillary length, high frequency precursors propagate ahead of the "main signal" and their period and amplitude, measured at a fixed point, increase in time. For larger depths, low frequency "precursors" follow the main signal with a decreasing period and amplitude. These behaviors are understood in the framework of the analysis first introduced for linear transient electromagnetic waves in a dielectric medium by Sommerfeld [Ann. Phys. (Leipzig) 44, 177 (1914)]] and Brillouin [Ann. Phys. (Leipzig) 44, 203 (1914)]].

We report an experimental study of the scattering of sound by sound in the vicinity of the liquid-vapor critical point of carbon dioxide. We measure the amplitude of the scattered difference frequency wave generated by acoustic bulk nonlinearities. We observe that it is strongly increased in the vicinity of the critical point.

We report an experimental study of the magnetic field B--> induced by a turbulent swirling flow of liquid sodium submitted to a transverse magnetic field B-->(0). We show that the induced field can behave nonlinearly as a function of the magnetic Reynolds number, R(m). At low R(m), the induced mean field along the axis of the flow, , and the one parallel to B-->(0), , first behave like R(2)(m), whereas the third component, , is linear in R(m). The sign of is determined by the flow helicity. At higher R(m), B--> strongly depends on the local geometry of the mean flow: decreases to zero in the core of the swirling flow but remains finite outside. We compare the experimental results with the computed magnetic induction due to the mean flow alone.

We report the observation of depression solitary surface waves on a layer of mercury when its depth is thin enough compared to the capillary length. These waves, as well as the well known elevation solitary waves, are studied with a new measurement technique using inductive sensors. The shape of the solitary waves, their amplitude-dependent velocity, and their damping rates by viscosity are found in good agreement with theoretical predictions.

We present experimental measurements of sound velocity and absorption in a commercial shaving foam. We observe that both quantities evolve with time as the foam coarsens increasing its mean bubble radius . By varying the acoustic frequency we probe the foam from the large wavelength regime, lambda approximately 1500, down to the scale lambda approximately 20. Sound absorption alpha varies significantly with both the foam age and the excitation frequency. After an initial transition time of 20 min, the attenuation per wavelength, alphalambda, varies linearly with the foam age. In addition, for evolution times smaller than approximately 90 min, we observe that alphalambda scales linearly with both foam age and frequency. From these scalings we show that the thermal dissipation mechanism is the dominant one. Sound velocity c is initially frequency independent but the medium becomes slightly dispersive as the foam coarsens. We observe that sound velocity depends on the evolution of the structure of the foam, even in the large wavelength regime. After 2 h of foam coarsening, c decreases at least by a factor of 20%, due to the softening of the foam. These facts are explained by considering the liquid matrix elasticity, due to the presence of surfactant molecules. A simple model of foam structure, combined with results of Biot's theory for porous media, gives both good qualitative and quantitative agreement with our experimental results in the low frequency regime.

We report an experimental study on the effect of an external multiplicative noise on a subcritical bifurcation leading to the parametric amplification of surface waves. We show that the probability density function of the wave amplitude in the presence of noise has two maxima that do not correspond to any of the deterministic states. When the deterministic forcing is varied in the presence of noise, these most probable values give two new branches in the bifurcation diagram that involve a much larger difference in oscillation amplitude. The bistable region is also strongly enlarged. This noise induced bistability can be understood in the general framework of noise induced transitions.

We used the liquid-vapor equilibrium of CO2 near its critical point (T(C)-T=1 to 150 mK) in order to study the stability of an interface between a gas and a liquid having close densities rho(L) approximately rho(V) when submitted to high frequency f (3-57.5 Hz) horizontal vibrations (of amplitude a from 0.1 to 2.5 mm). Above a given velocity threshold (2piaf )(0) we observed a "frozen wave," corresponding to an interface profile of sinelike shape which is stationary in the reference frame of the vibrated sample cell. By varying the vibration parameters, the surface tension, and the density difference between the two phases via the temperature, it was found that the wavelength and the amplitude of the stationary profile are both increasing functions of the frequency and of the amplitude of the vibration and that they are proportional to the capillary length. Our measurements are consistent with a model of inviscid and incompressible flow averaging the effect of the vibration over a period and leading to a Kelvin-Helmholtz-like instability mechanism due to the relative motion of the two fluids.