Lagrangian velocity fluctuations in fully developed turbulence: scaling, intermittency, and dynamics (original) (raw)

Long Time Correlations in Lagrangian Dynamics: A Key to Intermittency in Turbulence

Physical Review Letters, 2002

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.

Lagrangian Velocity Statistics in Turbulent Flows: Effects of Dissipation

Physical Review Letters, 2003

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 hmin ≈ 0.18 to hmax ≈ 1, as the signature of the highly intermittent nature of Lagrangian velocity fluctuations.

Multifractal statistics of Lagrangian velocity and acceleration in turbulence

2005

The statistical properties of velocity and acceleration fields along the trajectories of fluid particles transported by a fully developed turbulent flow are investigated by means of high resolution direct numerical simulations. We present results for Lagrangian velocity structure functions, the acceleration probability density function and the acceleration variance conditioned on the instantaneous velocity. These are compared with predictions of the multifractal formalism and its merits and limitations are discussed. Understanding the Lagrangian statistics of particles advected by a turbulent velocity field, u(x, t), is important both for its theoretical implications [1] and for applications, such as the development of phenomenological and stochastic models for turbulent mixing . Recently, several authors have attempted to describe Lagrangian statistics such as acceleration by constructing models based on equilibrium statistics (see e.g. , critically reviewed in [6]). In this letter we show how the multifractal formalism offers an alternative approach which is rooted in the phenomenology of turbulence. Here, we derive the Lagrangian statistics from the Eulerian statistics without introducing ad hoc hypotheses.

Intermittency of Velocity Time Increments in Turbulence

Physical Review Letters, 2005

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.

A phenomenological theory of Eulerian and Lagrangian velocity fluctuations in turbulent flows

Comptes Rendus Physique, 2012

A phenomenological theory of the fluctuations of velocity occurring in a fully developed homogeneous and isotropic turbulent flow is presented. The focus is made on the fluctuations of the spatial (Eulerian) and temporal (Lagrangian) velocity increments. The universal nature of the intermittency phenomenon as observed in experimental measurements and numerical simulations is shown to be fully taken into account by the multiscale picture proposed by the multifractal formalism, and its extensions to the dissipative scales and to the Lagrangian framework. The article is devoted to the presentation of these arguments and to their comparisons against empirical data. In particular, explicit predictions of the statistics, such as probability density functions and high order moments, of the velocity gradients and acceleration are derived. In the Eulerian framework, at a given Reynolds number, they are shown to depend on a single parameter function called the singularity spectrum and to a universal constant governing the transition between the inertial and dissipative ranges. The Lagrangian singularity spectrum compares well with its Eulerian counterpart by a transformation based on incompressibility, homogeneity and isotropy and the remaining constant is shown to be difficult to estimate on empirical data. It is finally underlined the limitations of the increment to quantify accurately the singular nature of Lagrangian velocity. This is confirmed using higher order increments unbiased by the presence of linear trends, as they are observed on velocity along a trajectory.

The Turbulent Lagrangian Dissipative Particle Velocity Statistics

Mediterranean Journal of Basic and Applied Sciences (MJBAS), 2022

A statistical description of turbulence comprising a probability distribution for stationary flows is the basis for determining the nature of turbulent velocity fluctuations. Away from the Eulerian spatial increments of the velocity field, the Lagrangian notion of temporal velocity increments along particle trajectories appears to be the hob of turbulent velocity statistics, ostensibly in the presence of inherent intermittencies observable in particle tracking. Such intermittencies were analyzed by using the well-known velocity structure functions, which defer to the Kolmogorov similarity theory (KST). Since particle trajectories, under normal circumstances, submit to Gaussian statistics, the deviations from Kolmogorov similarity theory are considered a culprit in the event of intermittency.

Universal Intermittent Properties of Particle Trajectories in Highly Turbulent Flows

Physical Review Letters, 2008

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 2 120:740. 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.

Lagrangian Description of Turbulence

Les Houches - Ecole d’Ete de Physique Theorique, 2001

To describe transport of scalar and vector fields by a random flow one needs to apply the methods of statistical mechanics to the motion of fluid particles, i.e. to the Lagrangian dynamics. We first present the propagators describing evolving probability distributions of different configurations of fluid particles. We then use those propagators to describe growth, decay and steady states of different scalar and vector quantities transported by random flows. We discuss both practical questions like mixing and segregation and fundamental problems like symmetry breaking in turbulence. Contents I. Introduction A. Propagators B. Kraichnan model C. Large Deviation Approach II. Particles in fluid turbulence A. Single-particle diffusion B. Two-particle dispersion in a spatially smooth velocity C. Two-particle dispersion in a non-smooth incompressible flow D. Two-particle dispersion in a compressible flow E. Multi-particle configurations and zero modes III. Unforced evolution of passive fields A. Decay of tracer fluctuations B. Growth of density fluctuations in compressible flow C. Vector fields in a smooth velocity IV. Cascades of a passive tracer A. Direct cascade B. Inverse cascade in a compressible flow V. Active tracers A. Activity changing cascade direction B. Two-dimensional incompressible turbulence VI. Conclusion References