Fourier analysis of wave turbulence in a thin elastic plate

The spatio-temporal dynamics of the deformation of a vibrated plate is measured by a high speed Fourier transform profilometry technique. The space-time Fourier spectrum is analyzed. It displays a behavior consistent with the premises of the Weak Turbulence theory. A isotropic continuous spectrum of waves is excited with a non linear dispersion relation slightly shifted from the linear dispersion relation. The spectral width of the dispersion relation is also measured. The non linearity of this system is weak as expected from the theory. Finite size effects are discussed. Despite a qualitative agreement with the theory, a quantitative mismatch is observed which origin may be due to the dissipation that ultimately absorbs the energy flux of the Kolmogorov-Zakharov casade.Comment: accepted for publication in European Physical Journal B see http://www.epj.or

The 3D structure of the Lagrangian acceleration in turbulent flows

We report experimental results on the three dimensional Lagrangian acceleration in highly turbulent flows. Tracer particles are tracked optically using four silicon strip detectors from high energy physics that provide high temporal and spatial resolution. The components of the acceleration are shown to be statistically dependent. The probability density function (PDF) of the acceleration magnitude is comparable to a log-normal distribution. Assuming isotropy, a log-normal distribution of the magnitude can account for the observed dependency of the components. The time dynamics of the acceleration components is found to be typical of the dissipation scales whereas the magnitude evolves over longer times, possibly close to the integral time scale.Comment: accepted for publication in Physical Review Letter

Acceleration and vortex filaments in turbulence

We report recent results from a high resolution numerical study of fluid particles transported by a fully developed turbulent flow. Single particle trajectories were followed for a time range spanning more than three decades, from less than a tenth of the Kolmogorov time-scale up to one large-eddy turnover time. We present some results concerning acceleration statistics and the statistics of trapping by vortex filaments.Comment: 10 pages, 5 figure

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 particule at a turbulent Reynolds number $R_{\lambda} = 740$. Its dynamics is analyzed with two decades of time resolution, below the Lagrangian correlation time. We observe that the Lagrangian velocity spectrum has a Lorentzian form $E^{L}(\omega) = u_{rms}^{2} T_{L} / (1 + (T_{L}\omega)^{2})$, in agreement with a Kolmogorov-like scaling in the inertial range. The probability density function (PDF) of the velocity time increments displays a change of shape from quasi-Gaussian a integral time scale to stretched exponential tails at the smallest time increments. This intermittency, when measured from relative scaling exponents of structure functions, is more pronounced than in the Eulerian framework.Comment: 4 pages, 5 figures. to appear in PR

Lagrangian Velocity Statistics in Turbulent Flows: Effects of Dissipation

We use the multifractal formalism to describe the effects of dissipation on Lagrangian velocity statistics in turbulent flows. We analyze high Reynolds number experiments and direct numerical simulation (DNS) data. We show that this approach reproduces the shape evolution of velocity increment probability density functions (PDF) from Gaussian to stretched exponentials as the time lag decreases from integral to dissipative time scales. A quantitative understanding of the departure from scaling exhibited by the magnitude cumulants, early in the inertial range, is obtained with a free parameter function D(h) which plays the role of the singularity spectrum in the asymptotic limit of infinite Reynolds number. We observe that numerical and experimental data are accurately described by a unique quadratic D(h) spectrum which is found to extend from $h_{min} \approx 0.18$ to $h_{max} \approx 1$, as the signature of the highly intermittent nature of Lagrangian velocity fluctuations.Comment: 5 pages, 3 figures, to appear in PR

Long time correlations in Lagrangian dynamics: a key to intermittency in turbulence

New aspects of turbulence are uncovered if one considers flow motion from the perspective of a fluid particle (known as the Lagrangian approach) rather than in terms of a velocity field (the Eulerian viewpoint). Using a new experimental technique, based on the scattering of ultrasounds, we have obtained a direct measurement of particle velocities, resolved at all scales, in a fully turbulent flow. It enables 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, we study a Langevin equation that incorporates these features and we show that the resulting dynamics accounts for the observed one- and two-point statistical properties of the Lagrangian velocity fluctuations. Our approach connects the intermittent statistical nature of turbulence to the dynamics of the flow.Comment: 4 pages, 4 figure

Intermittency of velocity time increments in turbulence

We analyze the statistics of turbulent velocity fluctuations in the time domain. Three cases are computed numerically and compared: (i) the time traces of Lagrangian fluid particles in a (3D) turbulent flow (referred to as the "dynamic" case); (ii) the time evolution of tracers advected by a frozen turbulent field (the "static" case), and (iii) the evolution in time of the velocity recorded at a fixed location in an evolving Eulerian velocity field, as it would be measured by a local probe (referred to as the "virtual probe" case). We observe that the static case and the virtual probe cases share many properties with Eulerian velocity statistics. The dynamic (Lagrangian) case is clearly different; it bears the signature of the global dynamics of the flow.Comment: 5 pages, 3 figures, to appear in PR

Transport of magnetic field by a turbulent flow of liquid sodium

We study the effect of a turbulent flow of liquid sodium generated in the von K\'arm\'an 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.Comment: 4 pages, 6 figure

Capture of particles of dust by convective flow

Interaction of particles of dust with vortex convective flows is under theoretical consideration. It is assumed that the volume fraction of solid phase is small, variations of density due to nonuniform distribution of particles and those caused by temperature nonisothermality of medium are comparable. Equations for the description of thermal buoyancy convection of a dusty medium are developed in the framework of the generalized Boussinesq approximation taking into account finite velocity of particle sedimentation. The capture of a cloud of dust particles by a vortex convective flow is considered, general criterion for the formation of such a cloud is obtained. The peculiarities of a steady state in the form of a dust cloud and backward influence of the solid phase on the carrier flow are studied in detail for a vertical layer heated from the sidewalls. It is shown that in the case, when this backward influence is essential, a hysteresis behavior is possible. The stability analysis of the steady state is performed. It turns out that there is a narrow range of governing parameters, in which such a steady state is stable.Comment: 14 pages, 10 figures, published in Physics of Fluid