Clustering of floaters on the free surface of a turbulent flow: an experimental study

We present an experimental study of the statistical properties of millimeter-size spheres floating on the surface of a turbulent flow. The flow is generated in a layer of liquid metal by an electromagnetic forcing. By using two magnet arrays, we are able to create one highly fluctuating flow and another, more stationary flow. In both cases, we follow the motion of hundreds of particles floating at the deformed interface of the liquid metal. We evidence the clustering of floaters by a statistical study of the local concentration of particles. Some dynamical properties of clusters are exposed. We perform spatial correlations between particle concentration and hydrodynamical quantities linked with inertial effects; with vortical motion, and with horizontal divergence (corresponding to compressibility in the surface). From comparing these correlations, we propose the so-called surface compressibility as the main clustering mechanism in our system. Hence, although floaters are not passive scalar and move on a deformed surface, the scenario is similar to the one reported for passive scalar on an almost flat free surface of a turbulent flow.Comment: 11 pages, 7 figures. Accepted to publication in European Journal of Mechanics B/Fluid

Intermittency as a consequence of a stationarity constraint on the energy flux

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 reference

Low frequency spectra of bending wave turbulence

We study experimentally the dynamics of long waves among turbulent bending waves in a thin elastic plate set into vibration by a monochromatic forcing at a frequency $f_0$. This frequency is chosen large compared with the characteristic frequencies of bending waves. As a consequence, a range of conservative scales, without energy flux in average, exists for frequencies $f<f_0$. Within this range, we report a flat power density spectrum for the orthogonal velocity, corresponding to energy equipartition between modes. Thus, the average energy per mode $\beta^{-1}$ -- analogous to a temperature -- fully characterizes the large-scale turbulent wave field. We present an expression for $\beta$ as a function of the forcing frequency and amplitude, and of the plate characteristics

Spatio-temporal boundary dissipation measurement in Taylor-Couette flow using Diffusing-Wave Spectroscopy

Diffusing-Wave Spectroscopy (DWS) allows for the direct measurement of the squared strain-rate tensor. When combined with commonly available high-speed cameras, we show that DWS gives direct access to the spatio-temporal variations of the viscous dissipation rate of a Newtonian fluid flow. The method is demonstrated using a Taylor-Couette (TC) cell filled with a lipid emulsion or a \ch{TiO2} suspension. We image the boundary dissipation rate in a quantitative and time-resolved fashion by shining coherent light at the experimental cell and measuring the local correlation time of the speckle pattern. The results are validated by comparison with the theoretical prediction for an ideal TC flow and with global measurements using a photomultiplier tube and a photon correlator. We illustrate the method by characterizing the spatial organization of the boundary dissipation rate past the Taylor-Couette instability threshold, and its spatio-temporal dynamics in the wavy vortex flow that arises beyond a secondary instability threshold. This study paves the way for direct imaging of the dissipation rate in a large variety of flows, including turbulent ones.Comment: 12 pages, 6 figure

Velocity-informed upper bounds on the convective heat transport induced by internal heat sources and sinks

Three-dimensional convection driven by internal heat sources and sinks (CISS) leads to experimental and numerical scaling-laws compatible with a mixing-length - or `ultimate' - scaling regime $Nu \sim \sqrt{Ra}$. However, asymptotic analytic solutions and idealized 2D simulations have shown that laminar flow solutions can transport heat even more efficiently, with $Nu \sim Ra$. The turbulent nature of the flow thus has a profound impact on its transport properties. In the present contribution we give this statement a precise mathematical sense. We show that the Nusselt number maximized over all solutions is bounded from above by const.$\times Ra$, before restricting attention to 'fully turbulent branches of solutions', defined as families of solutions characterized by a finite nonzero limit of the dissipation coefficient at large driving amplitude. Maximization of $Nu$ over such branches of solutions yields the better upper-bound $Nu \lesssim \sqrt{Ra}$. We then provide 3D numerical and experimental data of CISS compatible with a finite limiting value of the dissipation coefficient at large driving amplitude. It thus seems that CISS achieves the maximal heat transport scaling over fully turbulent solutions

Statistics of injected power on a bouncing ball subjected to a randomly vibrating piston

International audienceWe present an experimental study on the statistical properties of the injected power needed to maintain an inelastic ball bouncing constantly on a randomly accelerating piston in the presence of gravity. We compute the injected power at each collision of the ball with the moving piston by measuring the velocity of the piston and the force exerted on the piston by the ball. The probability density function of the injected power has its most probable value close to zero and displays two asymmetric exponential tails, depending on the restitution coefficient, the piston acceleration, and its frequency content. This distribution can be deduced from a simple model assuming quasi-Gaussian statistics for the force and velocity of the piston

Effects of the low frequencies of noise on On-Off intermittency

A bifurcating system subject to multiplicative noise can exhibit on-off intermittency close to the instability threshold. For a canonical system, we discuss the dependence of this intermittency on the Power Spectrum Density (PSD) of the noise. Our study is based on the calculation of the Probability Density Function (PDF) of the unstable variable. We derive analytical results for some particular types of noises and interpret them in the framework of on-off intermittency. Besides, we perform a cumulant expansion for a random noise with arbitrary power spectrum density and show that the intermittent regime is controlled by the ratio between the departure from the threshold and the value of the PSD of the noise at zero frequency. Our results are in agreement with numerical simulations performed with two types of random perturbations: colored Gaussian noise and deterministic fluctuations of a chaotic variable. Extensions of this study to another, more complex, system are presented and the underlying mechanisms are discussed.Comment: 13pages, 13 figure

Fluctuations of energy flux in wave turbulence

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.Comment: submitted to PR

Experimental Observation of Spatially Localized Dynamo Magnetic Fields

International audienceWe 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 Ka ́rma ́n 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