Lagrangian dispersion and heat transport in convective turbulence

Lagrangian studies of the local temperature mixing and heat transport in turbulent Rayleigh-Bénard convection are presented, based on three-dimensional direct numerical simulations. Contrary to vertical pair distances, the temporal growth of lateral pair distances agrees with the Richardson law, but yields a smaller Richardson constant due to correlated pair motion in plumes. Our results thus imply that Richardson dispersion is also found in anisotropic turbulence. We find that extremely large vertical accelerations appear less frequently than lateral ones and are not connected with rising or falling thermal plumes. The height-dependent joint Lagrangian statistics of vertical acceleration and local heat transfer allow us to identify a zone which is dominated by thermal plume mixing.     

Stochastic jets and nonhomogeneous transport in Lagrangian turbulence

Computer simulations are presented for a new object of chaos, stochastic jets, for a steady flow with five-fold symmetry with the Beltrami property. Lagrangian chaos of streamlines can reveal itself in the existence of huge flights which is connected with the asymptotic laws of anomalous transport of passive particles.     

Nondiffusive transport in plasma turbulence: a fractional diffusion approach

Numerical evidence of nondiffusive transport in three-dimensional, resistive pressure-gradient-driven plasma turbulence is presented. It is shown that the probability density function (pdf) of tracer particles' radial displacements is strongly non-Gaussian and exhibits algebraic decaying tails. To model these results we propose a macroscopic transport model for the pdf based on the use of fractional derivatives in space and time that incorporate in a unified way space-time nonlocality (non-Fickian transport), non-Gaussianity, and nondiffusive scaling. The fractional diffusion model reproduces the shape and space-time scaling of the non-Gaussian pdf of turbulent transport calculations. The model also reproduces the observed superdiffusive scaling.     

Multifractal dimension of Lagrangian turbulence

We report experimental measurements of the Lagrangian multifractal dimension spectrum in an intensely turbulent laboratory water flow by the optical tracking of tracer particles. The Legendre transform of the measured spectrum is compared with measurements of the scaling exponents of the Lagrangian velocity structure functions, and excellent agreement between the two measurements is found, in support of the multifractal picture of turbulence. These measurements are compared with three model dimension spectra. When the nonexistence of structure functions of order less than -1 is accounted for, the models are shown to agree well with the measured spectrum.     

Lagrangian dynamics of drift-wave turbulence

The statistical properties of Lagrangian particle transport are investigated in dissipative drift-wave turbulence modelled by the Hasegawa-Wakatani system. By varying the adiabaticity parameter c, the flow regime can be modified from a hydrodynamic limit for c=0 to a geostrophic limit for c→∞. For c of order unity the quasi-adiabatic regime is obtained, which might be relevant to describe the edge turbulence of fusion plasmas in tokamaks. This particularity of the model allows one to study the change in dynamics when varying from one turbulent flow regime to another. By means of direct numerical simulation we consider four values for c and show that the Lagrangian dynamics is most intermittent in the hydrodynamic regime, while the other regimes are not or only weakly intermittent. In both quasi-adiabatic and quasi-geostrophic regimes the PDFs of acceleration exhibit exponential tails. This behaviour is due to the pressure term in the acceleration and not a signature of intermittency.     

Lagrangian structure functions in hydrodynamic turbulence

Based on a solution of the Navier-Stokes equations for the inertial range of fully developed turbulence, a statistical theory is developed to determine the Lagrangian structure functions K _n (τ). Over times τ shorter than the large-scale correlation time τ_c, they obey scaling relations of the form K _n (τ) ∞ \(\tau ^{\zeta _n } \). Analytical expressions are derived for ζ _n . A detailed comparison between the theory and the experimental results presented in [1] demonstrates complete quantitative agreement. A new concept is introduced in turbulence theory: the correlation R _n (τ) between tracer-particle positions on a Lagrangian trajectory. It is shown that the position correlation functions R _n exhibit universal scaling behavior for n > 3.     

Measurement of turbulence decorrelation during transport barrier evolution in a high-temperature fusion plasma

A low power polychromatic beam of microwaves is used to diagnose the behavior of turbulent fluctuations in the core of the JT-60U tokamak during the evolution of the internal transport barrier. A continuous reduction in the size of turbulent structures is observed concomitant with the reduction of the density scale length during the evolution of the internal transport barrier. The density correlation length decreases to the order of the ion gyroradius, in contrast with the much longer scale lengths observed earlier in the discharge, while the density fluctuation level remain similar to the level before transport barrier formation.     

Uncovering the Lagrangian skeleton of turbulence

We present a technique that uncovers the Lagrangian building blocks of turbulence, and apply this technique to a quasi-two-dimensional turbulent flow experiment. Our analysis identifies an intricate network of attracting and repelling material lines. This chaotic tangle, the Lagrangian skeleton of turbulence, shows a level of complexity found previously only in theoretical and numerical examples of strange attractors. We quantify the strength (hyperbolicity) of each material line in the skeleton and demonstrate dramatically different mixing properties in different parts of the tangle.     

Lagrangian turbulence in nonstationary 2-D flows

Lagrangian particle transport in nonstationary 2-D flows is studied both analytically and numerically. Analytic expressions for the diffusion coefficients are obtained for the adiabatic regime. Numerical estimates of the diffusion coefficients are found to agree with the theoretical results.     

High order Lagrangian velocity statistics in turbulence

We report measurements of the Lagrangian velocity structure functions of orders 1 through 10 in a high Reynolds number (Taylor microscale Reynolds numbers of up to R(lambda) = 815 ) turbulence experiment. Passive tracer particles are tracked optically in three dimensions and in time, and velocities are calculated from the particle tracks. The structure function anomalous scaling exponents are measured both directly and using extended self-similarity and are found to be more intermittent than their Eulerian counterparts. Classical Kolmogorov inertial range scaling is also found for all structure function orders at times that trend downward as the order increases. The temporal shift of this classical scaling behavior is observed to saturate as the structure function order increases at times shorter than the Kolmogorov time scale.     

Thermal parametric turbulence in a plasma

A theory of thermal parametric instability (TPI) in an inhomogeneous magnetoplasma is developed. The threshold pump wave amplitude and increments of TPI are obtained. The spacial spectra of plasma waves and magnetic field aligned density perturbations are determined at the nonlinear stage of TPI, perturbation intensity dependence on pump energy is also analyzed. The theoretical results are applied to explain the ionospheric modification experiments.     

Scaling laws for plasma transport due toη i-driven turbulence

The scale invariance technique has been employed to discuss theη _i-driven turbulent transport under a new fluid model developed by Kimet al [1]. Our analysis reveals that the finite Larmour radius effect plays a decisive role to determine the scaling behaviour of the energy transport under the new fluid model. However, the overall scaling of the transport coefficient remains unchanged as compared to that derived by Connor [2] under the traditional fluid model. The approximations considered by Connor [2] are qualified with additional requirements within the new fluid approach. In the dissipative case, which has not been discussed earlier, additional constraints on the power scaling laws of the transport properties are imposed due to the dissipative mechanisms in the basic governing equations.     

Self-regulation of E x B flow shear via plasma turbulence

The momentum balance has been applied to the ExB flow in the edge region of a reversed field pinch (RFP) configuration. All terms, including those involving fluctuations, have been measured in stationary condition in the edge region of the Extrap-T2R RFP experiment. It is found that the component of the Reynolds stress driven by electrostatic fluctuations is the term playing the major role in driving the shear of the ExB flow to a value marginal for turbulent suppression, so that the results are in favor of a turbulence self-regulating mechanism underlying the momentum balance at the edge. Balancing the sheared flow driving and damping terms, the plasma viscosity is found anomalous and consistent with the diffusivity due to electrostatic turbulence.     

Multifractal statistics of Lagrangian velocity and acceleration in turbulence

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.