ABSTRACT
The Superfluid High REynolds von Kármán experiment facility exploits the capacities of a high cooling power refrigerator (400 W at 1.8 K) for a large dimension von Kármán flow (inner diameter 0.78 m), which can work with gaseous or subcooled liquid (He-I or He-II) from room temperature down to 1.6 K. The flow is produced between two counter-rotating or co-rotating disks. The large size of the experiment allows exploration of ultra high Reynolds numbers based on Taylor microscale and rms velocity [S. B. Pope, Turbulent Flows (Cambridge University Press, 2000)] (Rλ > 10000) or resolution of the dissipative scale for lower Re. This article presents the design and first performance of this apparatus. Measurements carried out in the first runs of the facility address the global flow behavior: calorimetric measurement of the dissipation, torque and velocity measurements on the two turbines. Moreover first local measurements (micro-Pitot, hot wire, ) have been installed and are presented.
ABSTRACT
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.
ABSTRACT
The local statistical and geometric structure of three-dimensional turbulent flow can be described by the properties of the velocity gradient tensor. A stochastic model is developed for the Lagrangian time evolution of this tensor, in which the exact nonlinear self-stretching term accounts for the development of well-known non-Gaussian statistics and geometric alignment trends. The nonlocal pressure and viscous effects are accounted for by a closure that models the material deformation history of fluid elements. The resulting stochastic system reproduces many statistical and geometric trends observed in numerical and experimental 3D turbulent flows, including anomalous relative scaling.
ABSTRACT
We perform a statistical analysis of experimental fully developed turbulence longitudinal velocity data in the Fourier space. We address the controversial issue of statistical intermittency of spatial Fourier modes by acting on the finite spectral resolution. We derive a link between velocity structure functions and the flatness of Fourier modes thanks to cascade models. Similar statistical behaviors are recovered in the analysis of spatial Fourier modes of vorticity obtained in an acoustic scattering experiment. We conclude that vorticity is long-range correlated and found more intermittent than longitudinal velocity.
ABSTRACT
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); (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.
ABSTRACT
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 data. We show that this approach reproduces the shape evolution of velocity increment probability density functions 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) approximately 0.18 to h(max) approximately 1.
