Multiparticle dispersion in fully developed turbulence

Physical Review Letters, 2000

Physics of Fluids, 2005

We present a detailed investigation of the particle pair separation process in homogeneous isotropic turbulence. We use data from direct numerical simulations up to R λ ∼ 280 following the evolution of about two million passive tracers advected by the flow over a time span of about three decades. We present data for both the separation distance and the relative velocity statistics. Statistics are measured along the particle pair trajectories both as a function of time and as a function of their separation, i.e. at fixed scales. We compare and contrast both sets of statistics in order to gain an insight into the mechanisms governing the separation process. We find very high levels of intermittency in the early stages, that is, for travel times up to order ten Kolmogorov time scales. The fixed scale statistics allow us to quantify anomalous corrections to Richardson diffusion in the inertial range of scales for those pairs that separate rapidly. It also allows a quantitative analysis of intermittency corrections for the relative velocity statistics.

Journal of Physics: Conference Series, 2011

Spatial and velocity statistics of heavy point-like particles in incompressible, homogeneous, and isotropic three-dimensional turbulence is studied by means of direct numerical simulations at two values of the Taylor-scale Reynolds number Re λ ∼ 200 and Re λ ∼ 400, corresponding to resolutions of 512 3 and 2048 3 grid points, respectively. Particles Stokes number values range from St ≈ 0.2 to 70. Stationary small-scale particle distribution is shown to display a singular-multifractal-measure, characterized by a set of generalized fractal dimensions with a strong sensitivity on the Stokes number and a possible, small Reynolds number dependency. Velocity increments between two inertial particles depend on the relative weight between smooth events-where particle velocity is approximately the same of the fluid velocity-, and caustic contributions-when two close particles have very different velocities. The latter events lead to a non-differentiable small-scale behaviour for the relative velocity. The relative weight of these two contributions changes at varying the importance of inertia. We show that moments of the velocity difference display a quasi bi-fractal-behavior and that the scaling properties of velocity increments for not too small Stokes number are in good agreement with a recent theoretical prediction made by K. Gustavsson and B. Mehlig arXiv:1012.1789v1 [physics.fludyn], connecting the saturation of velocity scaling exponents with the fractal dimension of particle clustering.

Reviews of Modern Physics, 2001

The understanding of fluid turbulence has considerably progressed in recent years. The application of the methods of statistical mechanics to the description of the motion of fluid particles, i.e. to the Lagrangian dynamics, has led to a new quantitative theory of intermittency in turbulent transport. The first analytical description of anomalous scaling laws in turbulence has been obtained. The underlying physical mechanism reveals the role of statistical integrals of motion in non-equilibrium systems. For turbulent transport, the statistical conservation laws are hidden in the evolution of groups of fluid particles and arise from the competition between the expansion of a group and the change of its geometry. By breaking the scaleinvariance symmetry, the statistically conserved quantities lead to the observed anomalous scaling of transported fields. Lagrangian methods also shed new light on some practical issues, such as mixing and turbulent magnetic dynamo.

Journal Homepage: http://pof.aip.org/ Journal Information: http://pof.aip.org/about/about_the_journal Top downloads: http://pof.aip.org/features/most_downloaded Information for Authors: http://pof.aip.org/authors Downloaded 22 Jul 2013 to 143.215.126.126. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://pof.aip.org/about/rights_and_permissions A wide range of relative two-particle dispersion statistics from the Lagrangian Kinematic Simulation KS model, which contains turbulent-like flow structures, compares well with Yeung's Phys. Fluids 6, 3416 1994 DNS results. In particular, the Lagrangian flatness factor 4 (t) compares excellently better than Heppe's J. Fluid Mech. 357, 167 1998 nonlinear stochastic model. For higher Reynolds numbers the results from KS show that 4 (t) is significantly greater than 3 over a wide range of times within the inertial range of time scales.

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

We obtain, by extensive direct numerical simulations, trajectories of heavy inertial particles in two-dimensional, statistically steady, homogeneous, and isotropic turbulent flows, with friction. We show that the probability distribution function P(κ), of the trajectory curvature κ, is such that, as κ → ∞, P(κ) ∼ κ −hr , with hr = 2.07 ± 0.09. The exponent hr is universal, insofar as it is independent of the Stokes number St and the energy-injection wave number kinj. We show that this exponent lies within error bars of their counterparts for trajectories of Lagrangian tracers. We demonstrate that the complexity of heavy-particle trajectories can be characterized by the number NI(t, St) of inflection points (up until time t) in the trajectory and nI(St

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.

2003

As three particles are advected by a turbulent flow, they separate from each other and develop non trivial geometries, which effectively reflect the structure of the turbulence. We investigate here the geometry, in a statistical sense, of three Lagrangian particles advected, in 2-dimensions, by Kinematic Simulation (KS). KS is a Lagrangian model of turbulent diffusion that makes no use of any delta correlation in time at any level. With this approach, situations with a very large range of inertial scales and varying persistence of spatial flow structure can be studied. We first show numerically that the model flow reproduces recent experimental results at low Reynolds numbers. The statistical properties of the shape distribution at much higher Reynolds number is then considered. Even at the highest available inertial range, of scale, corresponding to a ratio between large and small scales of $L/\eta \approx 17,000$, we find that the radius of gyration of the three points does not pr...

We uncover universal statistical properties of the trajectories of heavy inertial particles in three-dimensional, statistically steady, homogeneous, and isotropic turbulent flows by extensive direct numerical simulations. We show that the probability distribution functions (PDFs) P (φ), of the angle φ between the Eulerian velocity u and the particle velocity v, at this point and time, shows a power-law region in which P (φ) ∼ φ −γ , with a new universal exponent γ ≃ 4. Furthermore, the PDFs of the trajectory curvature κ and modulus θ of the torsion ϑ have power-law tails that scale, respectively, as P (κ) ∼ κ −hκ , as κ → ∞, and P (θ) ∼ θ −h θ , as θ → ∞, with exponents hκ ≃ 2.5 and h θ ≃ 3 that are universal to the extent that they do not depend on the Stokes number St (given our error bars). We also show that γ, hκ and h θ can be obtained by using simple stochastic models. We characterize the complexity of heavy-particle trajectories by the number NI(t, St) of points (up until time t) at which ϑ changes sign. We show that nI(St) ≡ limt→∞ N I (t,St) t ∼ St −∆ , with ∆ ≃ 0.4 a universal exponent.