Nicolas Mordant

Measurement of Lagrangian Velocity in Fully Developed Turbulence

We have developed a new experimental technique to measure the Lagrangian velocity of tracer particles in a turbulent flow, based on ultrasonic Doppler tracking. This method yields a direct access to the velocity of a single particle at a turbulent Reynolds number R(lambda) = 740, with two decades of time resolution, below the Lagrangian correlation time. We observe that the Lagrangian velocity spectrum has a Lorentzian form E(L)(omega) = u(2)(rms)T(L)/[1+(T(L)omega)(2)], in agreement with a Kolmogorov-like scaling in the inertial range. The probability density functions of the velocity time increments display an intermittency which is more pronounced than that of the corresponding Eulerian spatial increments.

Generation of a magnetic field by dynamo action in a turbulent flow of liquid sodium

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.

Magnetic field reversals in an experimental turbulent dynamo

We report the first experimental observation of reversals of a dynamo field generated in a laboratory experiment based on a turbulent flow of liquid sodium. The magnetic field randomly switches between two symmetric solutions B and -B. We observe a hierarchy of time scales similar to the Earths magnetic field: the duration of the steady phases is widely distributed, but is always much longer than the time needed to switch polarity. In addition to reversals we report excursions. Both coincide with minima of the mechanical power driving the flow. Small changes in the flow driving parameters also reveal a large variety of dynamo regimes.

Experimental and numerical study of the Lagrangian dynamics of high Reynolds turbulence

We introduce an original acoustic method to track the motion of tracer particles in high Reynolds number turbulent flows. We present in detail the experimental technique and show that it yields a measurement of the Lagrangian velocity variations of single particles, resolved across the inertial range turbulence. Second-order quantities such as the velocity autocorrelation function and time spectrum are in agreement with Kolmogorov 1941 phenomenology. Higher-order quantities reveal a very strong intermittency in the Lagrangian dynamics. Using both the results of the measurements and of direct numerical simulations, we show that the origin of intermittency can be traced back to the existence of long-time correlations in the dynamics of the Lagrangian acceleration. Finally, we discuss the role played by vortices in the Lagrangian dynamics.

Universal intermittent properties of particle trajectories in highly turbulent flows

We present a collection of eight data sets from state-of-the-art experiments and numerical simulations on turbulent velocity statistics along particle trajectories obtained in different flows with Reynolds numbers in the range R{lambda}in[120:740]. Lagrangian structure functions from all data sets are found to collapse onto each other on a wide range of time lags, pointing towards the existence of a universal behavior, within present statistical convergence, and calling for a unified theoretical description. Parisi-Frisch multifractal theory, suitably extended to the dissipative scales and to the Lagrangian domain, is found to capture the intermittency of velocity statistics over the whole three decades of temporal scales investigated here.

The von Karman Sodium experiment: Turbulent dynamical dynamos

The von Karman Sodium (VKS) experiment studies dynamo action in the flow generated inside a cylinder filled with liquid sodium by the rotation of coaxial impellers (the von Karman geometry). We first report observations related to the self-generation of a stationary dynamo when the flow forcing is R-pi-symmetric, i.e., when the impellers rotate in opposite directions at equal angular velocities. The bifurcation is found to be supercritical with a neutral mode whose geometry is predominantly axisymmetric. We then report the different dynamical dynamo regimes observed when the flow forcing is not symmetric, including magnetic field reversals. We finally show that these dynamics display characteristic features of low dimensional dynamical systems despite the high degree of turbulence in the flow.

Long time correlations in lagrangian dynamics: a key to intermittency in turbulence.

Using a new experimental technique, based on the scattering of ultrasounds, we perform a direct measurement of particle velocities, in a fully turbulent flow. This allows us to approach intermittency in turbulence from a dynamical point of view and to analyze the Lagrangian velocity fluctuations in the framework of random walks. We find experimentally that the elementary steps in the walk have random uncorrelated directions but a magnitude that is extremely long range correlated in time. Theoretically, a Langevin equation is proposed and shown to account for the observed one- and two-point statistics. This approach connects intermittency to the dynamics of the flow.

Acceleration of heavy and light particles in turbulence: Comparison between experiments and direct numerical simulations

We compare experimental data and numerical simulations for the dynamics of inertial particles with finite density in turbulence. In the experiment, bubbles and solid particles are optically tracked in a turbulent flow of water using an Extended Laser Doppler Velocimetry technique. The probability density functions (PDF) of particle accelerations and their auto-correlation in time are computed. Numerical results are obtained from a direct numerical simulation in which a suspension of passive pointwise particles is tracked, with the same finite density and the same response time as in the experiment. We observe a good agreement for both the variance of acceleration and the autocorrelation time scale of the dynamics; small discrepancies on the shape of the acceleration PDF are observed. We discuss the effects induced by the finite size of the particles, not taken into account in the present numerical simulations.

Are there waves in elastic wave turbulence

An thin elastic steel plate is excited with a vibrator and its local velocity displays a turbulentlike Fourier spectrum. This system is believed to develop elastic wave turbulence. We analyze here the motion of the plate with a two-point measurement in order to check, in our real system, a few hypotheses required for the Zakharov theory of weak turbulence to apply. We show that the motion of the plate is indeed a superposition of bending waves following the theoretical dispersion relation of the linear wave equation. The nonlinearities seem to efficiently break the coherence of the waves so that no modal structure is observed. Several hypotheses of the weak turbulence theory seem to be verified, but nevertheless the theoretical predictions for the wave spectrum are not verified experimentally.

On the magnetic fields generated by experimental dynamos

We review the results obtained by three successful fluid dynamo experiments and discuss what has been learnt from them about the effect of turbulence on the dynamo threshold and saturation. We then discuss several questions that are still open and propose experiments that could be performed to answer some of them.