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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 new effect, such as the efficiency of liquid metal batteries., Comment: 14 pages, 13 figures

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 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., Comment: 5 pages, 4 figures, 23 references

The study of the transitions among different regimes in thermal convection has been an issue of paramount importance in fluid mechanics. While the bifurcations at low Rayleigh number, when the flow is laminar or moderately chaotic, have been fully understood for a long time, transitions at higher Rayleigh number are much more difficult to be clearly identified. Here, through a numerical study of the two-dimensional Rayleigh-B\'enard convection covering four decades in Rayleigh number for two different Prandtl numbers, we find a clear-cut transition by considering the fluctuations of the heat flux through a horizontal plane, rather than its mean value. More specifically, we have found that this sharp transition is displayed by a jump of the ratio of the root-mean-square fluctuations of the heat flux to its mean value and occurs at $Ra/Pr \approx 10^9$. Above the transition, this ratio is found to be constant in all regions of the flow, while taking different values in the bulk and at the boundaries. Below the transition instead, different behaviors are observed at the boundaries and in the bulk: at the boundaries, this ratio decreases with respect to the Rayleigh number whereas it is found to be constant in the bulk for all values of the Rayleigh number. Through this numerical evidence and an analytical reasoning we confirm what was already observed in experiments, that is the decrease of the ratio of root-mean-square fluctuations of the heat flux to its mean value, observed at the boundaries below the transition, can understood in terms of the law of large numbers., Comment: 20 pages, 8 figures

We report on the experimental study of axisymmetric gravity-capillary standing waves generated by a vertically vibrating ring partially immersed into a fluid. Different regimes of standing waves are highlighted at the basin center depending on the forcing parameters: linear, nonlinear, and ejection regimes. For weak forcing, the standing waves display a resonant response, close to a natural frequency of the circular basin, predicted by the linear theory. For stronger forcing, we observed that the experimental spatial profile of standing waves breaks the up-down symmetry, and is well described by a third-order nonlinear theory. When the forcing is further increased, the maximum height of the axisymmetric wave crest at the basin center is found to increase linearly with its wavelength, due to the saturation of its steepness, a result well captured by a proposed model.

The temporal and spatial evolution of dispersed media is a fundamental problem in a wide range of physicochemical systems, such as emulsions, suspensions and aerosols. These systems are multiphasic and involve compounds of different densities. They are therefore subject to the influence of gravity which determines the sedimentation rate of their dispersed phase. This effect can be dominant and prevent a detailed study of the phenomena occurring between the constituents themselves, such as the coalescence of drops in emulsions, the evaporation of droplets or the flocculation in suspensions. In this context, the Centre National d'Etudes Spatiales (CNES) has recently supported the development of a new instrument to produce populations of droplets, a few micrometers in radius, under controlled conditions with the objective of allowing a detailed study of their properties in microgravity conditions. The principle of this instrument is to generate, by a fast compression/expansion of air, populations of water droplets and to track their evolution by optical scanning tomography in transmission mode within a volume of approximately 2 mm3. Parabolic flight experiments have shown the possibility to generate and accurately follow the evolution of populations of several hundred droplets for more than 20 seconds. The first experimental results show that it is possible to study their evaporation kinetics or their motion when imposing Von Karman swirling flows. This work is part of the AEROSOL project of DECLIC-EVO supported by CNES and aims to help the understanding of cloud microphysics which remains a critical open problem in the context of global warming.

We investigate the statistics of phase fluctuations of an acoustic wave propagating through a turbulent flow in line of sight (LOS) configuration. Experiments are performed on a closed von Karman swirling flow whose boundaries are maintained at a constant temperature. In particular, we analyze the root mean square (RMS) and the power spectrum density (PSD) of phase fluctuations. A model is developed and analytical predictions obtained for these quantities using geometrical acoustics are shown to be in agreement with experimental observations.

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 $\bar{\Omega}\sim r^{-3/2}$. 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 $\text{Nu}_\Omega\propto\sqrt{\text{Ta}}$. 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., Comment: 6 pages, 5 figures, accepted in Phys. Rev. Lett

Even in the absence of externally applied temperature gradients, spontaneously generated temperature fluctuations arise in turbulent flows. We experimentally study these fluctuations in a closed von Karman swirling flow of air at Mach number of order $10^{-3}$, whose boundaries are maintained at a constant temperature. We observe intermittent peaks of low temperature correlated with pressure drops within the flow and show that they are caused by vorticity filaments. The measured ratio of temperature to pressure fluctuation agrees with the prediction based on adiabatic cooling within vortex cores. This experimental study shows that although the Mach number of the flow is small, there exist regions within the flow where compressible effects cannot be discarded in the equation for temperature and locally dominate the effect of viscous dissipation.

The flow of an electrically conducting fluid in a thin disc under the action of an azimuthal Lorentz force is studied experimentally. At small forcing, the Lorentz force is balanced by either viscosity or inertia, yielding quasi-Keplerian velocity profiles. For very large current and moderate magnetic field, we observe a new regime, fully turbulent, which exhibits large fluctuations and a Keplerian mean rotation profile $\Omega\sim \frac{\sqrt{IB}}{r^{3/2}}$. In this turbulent regime, the dynamics is typical of thin layer turbulence, characterized by a direct cascade of energy towards the small scales and an inverse cascade to large scale. Finally, at very large magnetic field, this turbulent flow bifurcates to a quasi-bidimensional turbulent flow involving the formation of a large scale condensate in the horizontal plane. These results are well understood as resulting from an instability of the B\"odewadt-Hartmann layers at large Reynolds number and discussed in the framework of similar astrophysical flows., Comment: 30 pages, 12 figures

We investigate the spatio-temporal 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 which 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.

We study the primary bifurcations of a two-dimensional Kolmogorov flow in a channel subject to boundary conditions chosen to mimic a parallel flow, i.e. periodic and free-slip boundary conditions in the streamwise and spanwise directions, respectively. The control parameter is the Reynolds number based on the friction coefficient, denoted as $Rh$. We find that as we increase $Rh$ the laminar steady flow goes through a degenerate Hopf bifurcation with both the oscillation frequency and the amplitude of the growing mode being zero at the threshold. A reduced four-mode model captures the scalings that are obtained from the numerical simulations. As we increase $Rh$ further we observe a secondary instability which excites the largest mode in the domain. The saturated amplitude of the largest mode is found to scale as a $3/2$ power-law of the distance to the threshold which is also explained using a low-dimensional model., Comment: 12 pages, 5 figures

Using the FLUIDICS (Fluid Dynamics in Space) experiment in the International Space Station, turbulence of capillary waves at the air-water interface is experimentally investigated in weightlessness. Capillary waves are excited in a spherical container partially filled with water and undergoing sinusoidal or random oscillations. The fluctuations of the interface, recorded with two capacitive probes are analyzed by means of the frequency power spectrum of wave elevation. For high enough forcing amplitudes, we report power-law spectra with exponents close to the prediction of weak wave turbulence theory. However, in this experiment the free-surface steepness is not small compared to 1 and thus the investigated regimes correspond to strongly nonlinear wave turbulence.

We study the bifurcations of the large scale jets in the turbulent regime of a forced shear flow using direct numerical simulations of the Navier-Stokes equations. The bifurcations are seen in the probability density function (PDF) of the largest scale mode with the control parameter being the Reynolds number based on the friction coefficient denoted as $Rh$. As one increases $Rh$ in the turbulent regime, the PDF of the large scale mode first bifurcates from a Gaussian to a bimodal behaviour, signifying the emergence of reversals of the large scale flow where the flow fluctuates between two distinct turbulent states. Further increase in $Rh$ leads to a bifurcation from bimodal to unimodal PDF which denotes the disappearance of the reversals of the largest scale mode. We attribute the latter transition to the long-time memory that the large scale flow exhibits related to low frequency $1/f^\alpha$ type of noise with $0 < \alpha < 2$. We also demonstrate that a minimal model with 15 modes, obtained from the truncated Euler equation, is able to capture the bifurcations of the large scale jets exhibited by the Navier-Stokes equations., Comment: 12 pages, 7 figures

A shear flow of liquid metal (Galinstan) is driven in an annular channel by counter-rotating traveling magnetic fields imposed at the endcaps. 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 $1/f^\alpha$ power law on several decades and are related to power-law probability distributions $P(\tau)\sim\tau^{-\beta}$ 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 $\alpha$ and $\beta$ 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., Comment: 5 pages, 7 figures

We have explored a concept for an advanced Normal-Conducting Radio-Frequency (NCRF) C-band linear accelerator (linac) structure to achieve a high gradient, high power e$^+$e$^-$ linear collider in the TeV class. This design study represents the first comprehensive investigation for an emerging class of distributed coupling accelerator topology exploring nominal cavity geometries, frequency and temperature of operation. The structure features internal manifolds for distributing RF power separately to each cell, permitting the full structure geometry to be designed for high shunt impedance and low breakdown. Optimized within operational constraints, we find that it is advantageous for the structure to be cooled directly by liquid nitrogen (LN), further increasing the shunt impedance. A crucial part of this design process has been cost optimization, which is largely driven by the cost of peak RF power. The first operation of a distributed coupling structure at cryogenic temperatures and the nominal operating gradient 120 MeV/m is also presented, demonstrating the feasibility of achieving high-gradient performance with a cryogenically-cooled normal-conducting accelerating structure.

The flow of an electrically conducting fluid driven by a traveling magnetic field imposed at the endcaps of a cylindrical annulus is numerically studied. At sufficiently large magnetic Reynolds number, the system undergoes a transition from synchronism with the traveling field to a stalled flow, similar to the one observed in electromagnetic pumps. A new type of boundary layer is identified for such electromagnetically-driven flows, that can be understood as a combination of Hartmann and Shercliff layers generated by the spatio-temporal variations of the magnetic field imposed at the boundaries. An energy budget calculation shows that energy dissipation mostly occurs within these boundary layers and we observe that the ohmic dissipation Db always overcomes the viscous dissipation Dv, suggesting the existence of an upper bound for the efficiency of electromagnetic pumps. Finally, we show that the destabilization of the flow occurs when both dissipations are nearly equal., Comment: 15 pages, 9 figures

We aim at studying gasodynamic vortex cooling in an analytically solvable, thermodynamically consistent model that can explain limitations on the cooling efficiency. To this end, we study a angular plus radial flow between two (co-axial) rotating permeable cylinders. Full account is taken of compressibility, viscosity and heat conductivity. For a weak inward radial flow the model qualitatively describes the vortex cooling effect|both in terms of temperature and of decrease of the stagnation enthalpy|seen in short uniflow vortex (Ranque) tubes. The cooling does not result from external work, and its efficiency is defined as the ratio of the lowest temperature reached adiabatically (for the given pressure gradient) to the actually reached lowest temperature. We show that for the vortex cooling the efficiency is strictly smaller than 1, but in another configuration with an outward radial flow, we found that the efficiency can be larger than 1. This is related to both the geometry and the finite heat conductivity., Comment: 16 pages, 8 figures

We consider 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.

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., Comment: 6 pages, 9 figures

It is shown that the Truncated Euler Equations, 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 2D Navier-Stokes flow with bottom friction and a spatially periodic forcing. In particular, the random reversals of the large scale circulation on the turbulent background involve bifurcations of the probability distribution function of the large-scale circulation velocity that are described by the related microcanonical distribution which displays transitions from gaussian to bimodal and broken ergodicity. A minimal 13-mode model reproduces these results., Comment: 6 pages, 2 figures

We report the experimental observation of $1/f^{\alpha}$ noise in quasi-bidimensionnal turbulence of an electromagnetically forced flow. The large scale velocity $U_L$ exhibits this power-law spectrum with $\alpha \simeq 0.7$ over a range of frequencies smaller than both the characteristic turn-over 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 $\alpha$., Comment: 5 pages, 6 figures published in Europhysics Letters (2015)

We report the experimental observation of $1/f$ fluctuations 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, $1/f$ 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 $1/f$ fluctuations., Comment: 10 pages, 9 figures published in Journal of Statistical Physics (2015)

The MHD flow driven by a travelling magnetic field (TMF) 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., Comment: 14 pages, 11 figures

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 turbulent ABC flows forced at different forcing wavenumbers $k_f$ simulated using a subgrid turbulent model. The critical magnetic Reynolds number $Rm_c^T$ decreases as the forcing wavenumber $k_f$ increases from the smallest allowed $k_{min}=1/L$. At large $k_f$ on the other hand, $Rm_c^T$ increases with the forcing wavenumber as $Rm_c^T \propto \sqrt{ k_f}$ in agreement with mean-field scaling prediction. At $k_f L\simeq 4$ an optimal wavenumber is reached where $Rm_c^T$ obtains its minimum value. At this optimal wavenumber $Rm_c^T$ is smaller by more than a factor of ten than the case forced in $k_f=1$. This leads to a reduction of the energy injection rate by three orders of magnitude when compared to the case that the system is forced in 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 non-helical 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., Comment: 5 pages, 4 figures