Fluid particle accelerations in fully developed turbulence

Time-resolved volumetric measurement of fine-scale coherent structures in turbulence

We present full volumetric (three-dimensional) time-resolved (+one-dimensional) measurements of the velocity field in a large water mixing tank, allowing us to assess spatial and temporal rotational energy (enstrophy) and turbulent energy dissipation intermittency. In agreement with previous studies, highly intermittent behavior is observed, with intense coherent flow structures clustering in the periphery of larger vortices. However, further to previous work the full volumetric measurements allow us to separate out the effects of advection from other effects, elucidating not only their topology but also the evolution of these intense events, through the local balance of stretching and diffusion. These findings contribute toward a better understanding of the intermittency phenomenon, which should pave the way for more accurate models of the small-scale motions based on an understanding of the underlying flow physics.

Simulation of particle mixing in turbulent channel flow due to intrinsic fluid velocity fluctuation

We combine a discrete-element-method simulation with a stochastic process to model the movement of spherical particles in a turbulent channel flow. With this model we investigate the mixing properties of two species of particles flowing through the channel. We find a linear increase of the mixing zone with the length of the pipe. Flows at different Reynolds number are studied. Below a critical Reynolds number at the Taylor microscale of around Rc ≈ 300 the mixing rate is strongly dependent on the Reynolds number. Above Rc the mixing rate stays nearly constant.

Tracking the dynamics of translation and absolute orientation of a sphere in a turbulent flow

We study the six-dimensional dynamics--position and orientation--of a large sphere advected by a turbulent flow. The movement of the sphere is recorded with two high-speed cameras. Its orientation is tracked using a novel, efficient algorithm; it is based on the identification of possible orientation "candidates" at each time step, with the dynamics later obtained from maximization of a likelihood function. Analysis of the resulting linear and angular velocities and accelerations reveal a surprising intermittency for an object whose size lies in the inertial range, close to the integral scale of the underlying turbulent flow.

Orientation cues for high-flying nocturnal insect migrants: do turbulence-induced temperature and velocity fluctuations indicate the mean wind flow?

Migratory insects flying at high altitude at night often show a degree of common alignment, sometimes with quite small angular dispersions around the mean. The observed orientation directions are often close to the downwind direction and this would seemingly be adaptive in that large insects could add their self-propelled speed to the wind speed, thus maximising their displacement in a given time. There are increasing indications that high-altitude orientation may be maintained by some intrinsic property of the wind rather than by visual perception of relative ground movement. Therefore, we first examined whether migrating insects could deduce the mean wind direction from the turbulent fluctuations in temperature. Within the atmospheric boundary-layer, temperature records show characteristic ramp-cliff structures, and insects flying downwind would move through these ramps whilst those flying crosswind would not. However, analysis of vertical-looking radar data on the common orientations of nocturnally migrating insects in the UK produced no evidence that the migrants actually use temperature ramps as orientation cues. This suggests that insects rely on turbulent velocity and acceleration cues, and refocuses attention on how these can be detected, especially as small-scale turbulence is usually held to be directionally invariant (isotropic). In the second part of the paper we present a theoretical analysis and simulations showing that velocity fluctuations and accelerations felt by an insect are predicted to be anisotropic even when the small-scale turbulence (measured at a fixed point or along the trajectory of a fluid-particle) is isotropic. Our results thus provide further evidence that insects do indeed use turbulent velocity and acceleration cues as indicators of the mean wind direction.

Implicit atomistic viscosities in smoothed particle hydrodynamics

We consider a standard microscopic analysis of the transport coefficients, commonly used in nonequilibrium molecular dynamics techniques, and apply it to the smoothed particle hydrodynamics method in steady-shear flow conditions. As previously suggested by Posch [Phys. Rev. E 52, 1711 (1995)], we observe the presence of nonzero microscopic (kinetic and potential) contributions to the total stress tensor in addition to its dissipative part coming from the discretization of the Navier-Stokes continuum equations. Accordingly, the dissipative part of the shear stress produces an output viscosity equal to the input model parameter. On the other hand, the nonzero atomistic viscosities can contribute significantly to the overall output viscosity of the method. In particular, it is shown that the kinetic part, which acts similarly to an average Reynolds-like stress, becomes dominant at very low viscous flows where large velocity fluctuations occur. Remarkably, in this kinetic regime the probability distribution function of the particle accelerations is in surprisingly good agreement with non-gaussian statistics observed experimentally.

Aspect ratio dependence of heat transfer and large-scale flow in turbulent convection

The heat transport and corresponding changes in the large-scale circulation (LSC) in turbulent Rayleigh–Bénard convection are studied by means of three-dimensional direct numerical simulations as a function of the aspect ratio Γ of a closed cylindrical cell and the Rayleigh number Ra. The Prandtl number is Pr = 0.7 throughout the study. The aspect ratio Γ is varied between 0.5 and 12 for a Rayleigh number range between 107 and 109. The Nusselt number Nu is the dimensionless measure of the global turbulent heat transfer. For small and moderate aspect ratios, the global heat transfer law Nu = A × Raβ shows a power law dependence of both fit coefficients A and β on the aspect ratio. A minimum of Nu(Γ) is found at Γ ≈ 2.5 and Γ ≈ 2.25 for Ra = 107 and Ra = 108, respectively. This is the point where the LSC undergoes a transition from a single-roll to a double-roll pattern. With increasing aspect ratio, we detect complex multi-roll LSC configurations in the convection cell. For larger aspect ratios Γ ≳ 8, our data indicate that the heat transfer becomes independent of the aspect ratio of the cylindrical cell. The aspect ratio dependence of the turbulent heat transfer for small and moderate Γ is in line with a varying amount of energy contained in the LSC, as quantified by the Karhunen–Loève or proper orthogonal decomposition (POD) analysis of the turbulent convection field. The POD analysis is conducted here by the snapshot method for at least 100 independent realizations of the turbulent fields. The primary POD mode, which replicates the time-averaged LSC patterns, transports about 50% of the global heat for Γ ≥ 1. The snapshot analysis enables a systematic disentanglement of the contributions of POD modes to the global turbulent heat transfer. Although the smallest scale – the Kolmogorov scale ηK – and the largest scale – the cell height H – are widely separated in a turbulent flow field, the LSC patterns in fully turbulent fields exhibit strikingly similar texture to those in the weakly nonlinear regime right above the onset of convection. Pentagonal or hexagonal circulation cells are observed preferentially if the aspect ratio is sufficiently large (Γ ≳ 8).

Lagrangian tracer dynamics in a closed cylindrical turbulent convection cell

Turbulent Rayleigh-Bénard convection in a closed cylindrical cell is studied in the Lagrangian frame of reference with the help of three-dimensional direct numerical simulations. The aspect ratio of the cell Γ is varied between 1 and 12, and the Rayleigh number Ra between 10(7) and 10(9). The Prandtl number Pr is fixed at 0.7. It is found that both the pair dispersion of the Lagrangian tracer particles and the statistics of the acceleration components measured along the particle trajectories depend on the aspect ratio for a fixed Rayleigh number for the parameter range covered in our studies. This suggests that large-scale circulations present in the convection cell affect the Lagrangian dynamics. Our findings are in qualitative agreement with existing Lagrangian laboratory experiments on turbulent convection.

The Lagrangian exploration module: an apparatus for the study of statistically homogeneous and isotropic turbulence

We present an apparatus that generates statistically homogeneous and isotropic turbulence with a mean flow that is less than 10% of the fluctuating velocity in a volume of the size of the integral length scale. The apparatus is shaped as an icosahedron where at each of the 12 vertices the flow is driven by independently controlled propellers. By adjusting the driving of the different propellers the isotropy and homogeneity of the flow can be tuned, while keeping the mean flow weak.

Lagrangian views on turbulent mixing of passive scalars

The Lagrangian view of passive scalar turbulence has recently produced interesting results and interpretations. Innovations in theory, experiments, simulations and data analysis of Lagrangian turbulence are reviewed here in brief. Part of the review is closely related to the so-called Kraichnan model for the advection of the passive scalar in synthetic turbulence. Possible implications for a better understanding of the passive scalar mixing in Navier-Stokes turbulence are also discussed.

Inference in particle tracking experiments by passing messages between images

Methods to extract information from the tracking of mobile objects/particles have broad interest in biological and physical sciences. Techniques based on simple criteria of proximity in time-consecutive snapshots are useful to identify the trajectories of the particles. However, they become problematic as the motility and/or the density of the particles increases due to uncertainties on the trajectories that particles followed during the images' acquisition time. Here, we report an efficient method for learning parameters of the dynamics of the particles from their positions in time-consecutive images. Our algorithm belongs to the class of message-passing algorithms, known in computer science, information theory, and statistical physics as belief propagation (BP). The algorithm is distributed, thus allowing parallel implementation suitable for computations on multiple machines without significant intermachine overhead. We test our method on the model example of particle tracking in turbulent flows, which is particularly challenging due to the strong transport that those flows produce. Our numerical experiments show that the BP algorithm compares in quality with exact Markov Chain Monte Carlo algorithms, yet BP is far superior in speed. We also suggest and analyze a random distance model that provides theoretical justification for BP accuracy. Methods developed here systematically formulate the problem of particle tracking and provide fast and reliable tools for the model's extensive range of applications.

Lagrangian refined Kolmogorov similarity hypothesis for gradient time evolution and correlation in turbulent flows

We study time evolution of velocity and pressure gradients in isotropic turbulence by quantifying their autocorrelation functions and decorrelation time scales. The Lagrangian analysis uses data in a public database generated by direct numerical simulation at a Reynolds number Re{lambda} approximately 433. It is confirmed that when averaging over the entire domain, correlation functions decay on time scales on the order of the global Kolmogorov turnover time scale. However, when performing the analysis in different subregions of the flow, turbulence intermittency leads to large spatial variability in the decay time scales. Remarkably, excellent collapse of the autocorrelation functions is recovered when using a locally defined Kolmogorov time scale. This provides new evidence for the validity of Kolmogorov's refined similarity hypothesis, but from a Lagrangian viewpoint that provides a natural frame to describe the dynamics of turbulence.

Three-dimensional turbulent relative dispersion by the Gledzer-Ohkitani-Yamada shell model

We study pair dispersion in a three-dimensional incompressible high Reynolds number turbulent flow generated by Fourier transforming the dynamics of the Gledzer-Ohkitani-Yamada (GOY) shell model into real space. We show that GOY shell model can successfully reproduce both the Batchelor and the Richardson-Obukhov regimes of turbulent relative dispersion. We also study how the crossover time scales with the initial separations of a particle pair and compare it to the prediction by Batchelor.

Experimental investigation of Lagrangian structure functions in turbulence

Lagrangian properties obtained from a particle tracking velocimetry experiment in a turbulent flow at intermediate Reynolds number are presented. Accurate sampling of particle trajectories is essential in order to obtain the Lagrangian structure functions and to measure intermittency at small temporal scales. The finiteness of the measurement volume can bias the results significantly. We present a robust way to overcome this obstacle. Despite no fully developed inertial range, we observe strong intermittency at the scale of dissipation. The multifractal model is only partially able to reproduce the results.

Exact relation between Eulerian and Lagrangian velocity increment statistics

We present a formal connection between Lagrangian and Eulerian velocity increment distributions which is applicable to a wide range of turbulent systems ranging from turbulence in incompressible fluids to magnetohydrodynamic turbulence. For the case of the inverse cascade regime of two-dimensional turbulence we numerically estimate the transition probabilities involved in this connection. In this context we are able to directly identify the processes leading to strongly non-Gaussian statistics for the Lagrangian velocity increments.

Lagrangian studies in convective turbulence

We present high-resolution direct numerical simulations of turbulent three-dimensional Rayleigh-Bénard convection with a focus on the Lagrangian properties of the flow. The volume is a Cartesian slab with an aspect ratio of four bounded by free-slip planes at the top and bottom and with periodic side walls. The turbulence is inhomogeneous with respect to the vertical direction. This manifests in different lateral and vertical two-particle dispersion and in a dependence of the dispersion on the initial tracer position for short and intermediate times. Similar to homogeneous isotropic turbulence, the dispersion properties depend in addition to the initial pair separation and yield a short-range Richardson-like scaling regime of two-particle dispersion for initial separations close to the Kolmogorov dissipation length. The Richardson constant is about half the value of homogeneous isotropic turbulence. The multiparticle statistics is very close to the homogeneous isotropic case. Clusters of four Lagrangian tracers show a clear trend to form flat, almost coplanar, objects in the long-time limit and deviate from the Gaussian prediction. Significant efforts have been taken to resolve the statistics of the acceleration components up to order four correctly. We find that the vertical acceleration is less intermittent than the lateral one. The joint statistics of the vertical acceleration with the local convective and conductive heat flux suggests that rising and falling thermal plumes are not associated with the largest acceleration magnitudes. It turns out also that the Nusselt number which is calculated in the Lagrangian frame converges slowly in time to the standard Eulerian one.

Point-vortex model for Lagrangian intermittency in turbulence

Experiments have shown that Lagrangian statistics in turbulent flows display Gaussianly distributed velocity values and non-Gaussianly distributed velocity differences or accelerations. Coherent flow structures in the form of vortices have often been proposed to play an important role in this behavior. Here we examine the origin of these statistics using both continuously stirred n -body point-vortex simulations and analytic random variable transformation in a simplified model of randomly distributed vortices. We conclude that Lagrangian velocity distributions can be understood in terms of dominant nearest vortex neighbor contributions. Accelerations likewise reflect vortical contributions, but at smallest temporal increment are dominated, not by the motion of the Lagrangian tracers, but by vorticity reconfiguration within the domain.

Variable-range projection model for turbulence-driven collisions

We discuss the relative speeds DeltaV of inertial particles suspended in a highly turbulent gas when the Stokes number, a dimensionless measure of their inertia, is large. We identify a mechanism giving rise to the distribution P(DeltaV) approximately exp(-C|DeltaV|(4/3)) (for some constant C). Our conclusions are supported by numerical simulations, and by the analytical solution of a model equation of motion. The results determine the rate of collisions between suspended particles. They are relevant to the hypothesized mechanism for formation of planets by aggregation of dust particles in circumstellar nebula.

Lagrangian statistics in forced two-dimensional turbulence

We report on simulations of two-dimensional turbulence in the inverse energy cascade regime. Focusing on the statistics of Lagrangian tracer particles, scaling behavior of the probability density functions of velocity fluctuations is investigated. The results are compared to the three-dimensional case. In particular an analysis in terms of compensated cumulants reveals the transition from a strong non-Gaussian behavior with large tails to Gaussianity. The reported computation of correlation functions for the acceleration components sheds light on the underlying dynamics of the tracer particles.

Universal intermittent properties of particle trajectories in highly turbulent flows

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.

Extreme Lagrangian acceleration in confined turbulent flow

A Lagrangian study of two-dimensional turbulence for two different geometries, a periodic and a confined circular geometry, is presented to investigate the influence of solid boundaries on the Lagrangian dynamics. It is found that the Lagrangian acceleration is even more intermittent in the confined domain than in the periodic domain. The flatness of the Lagrangian acceleration as a function of the radius shows that the influence of the wall on the Lagrangian dynamics becomes negligible in the center of the domain, and it also reveals that the wall is responsible for the increased intermittency. The transition in the Lagrangian statistics between this region, not directly influenced by the walls, and a critical radius which defines a Lagrangian boundary layer is shown to be very sharp with a sudden increase of the acceleration flatness from about 5 to about 20.

Lagrangian particle statistics in turbulent flows from a simple vortex model

The statistics of Lagrangian particles in turbulent flows is considered in the framework of a simple vortex model. Here, the turbulent velocity field is represented by a temporal sequence of Burgers vortices of different circulation, strain, and orientation. Based on suitable assumptions about the vortices' statistical properties, the statistics of the velocity increments is derived. In particular, the origin and nature of small-scale intermittency in this model is investigated both numerically and analytically. We critically compare our results to experimental studies.

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.

Writing in turbulent air

We describe a scheme of molecular tagging velocimetry in air in which nitric oxide (NO) molecules are created out of O2 and N2 molecules in the focus of a strong laser beam. The NO molecules are visualized a while later by laser-induced fluorescence. The precision of the molecular tagging velocimetry of gas flows is affected by the gradual blurring of the written patterns through molecular diffusion. In the case of turbulent flows, molecular diffusion poses a fundamental limit on the resolution of the smallest scales in the flow. We study the diffusion of written patterns in detail for our tagging scheme which, at short (micros) delay times is slightly anomalous due to local heating by absorption of laser radiation. We show that our experiments agree with a simple convection-diffusion model that allows us to estimate the temperature rise upon writing. Molecular tagging can be a highly nonlinear process, which affects the art of writing. We find that our tagging scheme is (only) quadratic in the intensity of the writing laser.

Behavior of heavy particles in isotropic turbulence

The motion of heavy particles in isotropic turbulence is investigated using direct numerical simulation. The statistics related to the velocity and acceleration of heavy particles for a wide range of Stokes numbers, defined as the ratio of the particle response time to the Kolmogorov time scale of turbulence (St=tau_{p}/tau_{eta}) , are investigated. A particular emphasis is placed on the statistics of the fluid experienced by heavy particles, which provide essential information on the dispersion of these particles. The integral time scale of the velocity correlation of fluid seen by the particles T_{f} , which determines the diffusivity of heavy particles, displays a complex behavior different from the Lagrangian integral time scale of fluid T_{L} . A plausible physical explanation for the behavior of the time scale is provided.

Acceleration correlations and pressure structure functions in high-reynolds number turbulence

We present measurements of fluid particle accelerations in turbulent water flow between counterrotating disks using three-dimensional Lagrangian particle tracking. By simultaneously following multiple particles with sub-Kolmogorov-time-scale temporal resolution, we measured the spatial correlation of fluid particle acceleration at Taylor microscale Reynolds numbers between 200 and 690. We also obtained indirect, nonintrusive measurements of the Eulerian pressure structure functions by integrating the acceleration correlations. Our measurements are in good agreement with the theoretical predictions of the acceleration correlations and the pressure structure function in isotropic high-Reynolds number turbulence by Obukhov and Yaglom in 1951 [Prikl. Mat. Mekh. 15, 3 (1951)]. The measured pressure structure functions display K41 scaling in the inertial range.

Turbulent transport of material particles: an experimental study of finite size effects

We present experimental Lagrangian statistics of finite sized, neutrally bouyant, particles transported in an isotropic turbulent flow. The particle's diameter is varied over turbulent inertial scales. Finite size effects are shown not to be trivially related to velocity intermittency. The global shape of the particle's acceleration probability density functions is not found to depend significantly on its size while the particle's acceleration variance decreases as it becomes larger in quantitative agreement with the classical k(-7/3) scaling for the spectrum of Eulerian pressure fluctuations in the carrier flow.

Interaction of solid particles with a tangle of vortex filaments in a viscous fluid

Homogeneous isotropic turbulence consists of coherent filamentary vortex structures superimposed to a more incoherent background. The question which we address is the effect of these structures on the dynamics of small, neutrally buoyant solid particles. Rather than generating the turbulence by direct numerical simulation (DNS) of the Navier-Stokes equations, we use a model of turbulence based entirely on viscous vortex filaments which interact via inertial forces and reconnect with each other. Using this model, we show that solid particles can become trapped around vortex filaments, something difficult to achieve with DNS. Unlike most studies, we have not neglected inviscid inertial effects. By comparing the Stokes, local, and convective components of the particle's acceleration, we also show that the convective part clearly identifies the trapping.

Instrumented tracer for Lagrangian measurements in Rayleigh-Bénard convection

We have developed novel instrumentation for making Lagrangian measurements of temperature in diverse fluid flows. A small neutrally buoyant capsule is equipped with on-board electronics which measures temperature and transmits the data via a wireless radio frequency link to a desktop computer. The device has 80 dB dynamic range, resolving millikelvin changes in temperature with up to 100 ms sampling time. The capabilities of these "smart particles" are demonstrated in turbulent thermal convection in water. We measure temperature variations as the particle is advected by the convective motion and analyze its statistics. Additional use of cameras allow us to track the particle position and to report here the first direct measurement of Lagrangian heat flux transfer in Rayleigh-Bénard convection. The device shows promise for opening new research in a broad variety of fluid systems.

Multiscale model of gradient evolution in turbulent flows

A multiscale model for the evolution of the velocity gradient tensor in turbulence is proposed. The model couples "restricted Euler" (RE) dynamics describing gradient self-stretching with a cascade model allowing energy exchange between scales. We show that inclusion of the cascade process is sufficient to regularize the finite-time singularity of the RE dynamics. Also, the model retains geometrical features of real turbulence such as preferential alignments of vorticity and joint statistics of gradient tensor invariants. Furthermore, gradient fluctuations are non-Gaussian, skewed in the longitudinal case, and derivative flatness coefficients are in good agreement with experimental data.

Statistics of three-dimensional lagrangian turbulence

We consider a superstatistical model for a Lagrangian tracer particle in a high-Reynolds-number turbulent flow. The analytical model predictions are in excellent agreement with recent experimental data for flow between counter-rotating disks. In particular, the predicted Lagrangian scaling exponents zeta_{j} agree well with the measured exponents reported in H. Xu et al. [Phys. Rev. Lett.10.1103/PhysRevLett.96.114503 96, 114503 (2006)]. The model also correctly predicts the shape of acceleration probability densities, correlation functions, statistical dependencies between components, and explains the fact that enstrophy lags behind dissipation.

Curvature of lagrangian trajectories in turbulence

We report measurements of the curvature of Lagrangian trajectories in an intensely turbulent laboratory water flow measured with a high-speed particle-tracking system. The probability density function (PDF) of the instantaneous curvature is shown to have robust power-law tails. We propose a model for the instantaneous curvature PDF, assuming that the acceleration and velocity are uncorrelated Gaussian random variables, and show that our model reproduces the tails of our measured PDFs. We also predict the scaling of the most probable vorticity magnitude in turbulence, assuming Heisenberg-Yaglom scaling. Finally, we average the curvature along trajectories and show that, by removing the effects of large-scale flow reversals, the filtered curvature reveals the turbulent features.

Real-time image compression for high-speed particle tracking

High-speed particle tracking with digital video creates very large data rates and as a result experimenters are forced to make compromises between spatial resolution, temporal resolution, and the duration over which data is acquired. The images produced in particle tracking experiments typically contain a large amount of black space with relatively few bright pixels and this suggests the possibility of image compression. This paper describes a system for real-time compression of high-speed video. A digital circuit placed between the camera (500 Hz, 1280 x 1024 pixels) and frame grabber compresses data in real-time by comparing input pixels with a threshold value and outputs a vector containing the brightness and position of the bright pixels. In a typical experiment, the compression ratio for an image ranges from 100 to 1000 and varies dynamically depending on the number of filtered pixels. The reduced data rate makes it possible to write directly to the hard disk. While previously data could only be acquired for 6.5 s into 4 GB of dedicated video RAM, the new system could acquire full resolution data continuously for up to a week into a 600 GB hard drive.

Lagrangian measurements of inertial particle accelerations in grid generated wind tunnel turbulence

We describe Lagrangian measurements of water droplets in grid generated wind tunnel turbulence at a Taylor Reynolds number of R(lambda)=250 and an average Stokes number (St) of approximately 0.1. The inertial particles are tracked by a high speed camera moving along the side of the tunnel at the mean flow speed. The standardized acceleration probability density functions of the particles have spread exponential tails that are narrower than those of a fluid particles (St approximately 0) and there is a decrease in the acceleration variance with increasing Stokes number. A simple vortex model shows that the inertial particles selectively sample the fluid field and are less likely to experience regions of the fluid undergoing the largest accelerations. Recent direct numerical simulations compare favorably with these first measurements of Lagrangian statistics of inertial particles in highly turbulent flows.

A speculative study of 23-order fractional Laplacian modeling of turbulence: some thoughts and conjectures

This study makes the first attempt to use the 23-order fractional Laplacian modeling of Kolmogorov -53 scaling of fully developed turbulence and enhanced diffusing movements of random turbulent particles. Nonlinear inertial interactions and molecular Brownian diffusivity are considered to be the bifractal mechanism behind multifractal scaling of moderate Reynolds number turbulence. Accordingly, a stochastic equation is proposed to describe turbulence intermittency. The 23-order fractional Laplacian representation is also used to model nonlinear interactions of fluctuating velocity components, and then we conjecture a fractional Reynolds equation, underlying fractal spacetime structures of Levy 23 stable distribution and the Kolmogorov scaling at inertial scales. The new perspective of this study is that the fractional calculus is an effective approach to modeling the chaotic fractal phenomena induced by nonlinear interactions.

The Role of Pair Dispersion in Turbulent Flow

Mixing and transport in turbulent flows-which have strong local concentration fluctuations-are essential in many natural and industrial systems including reactions in chemical mixers, combustion in engines and burners, droplet formation in warm clouds, and biological odor detection and chemotaxis. Local concentration fluctuations, in turn, are intimately tied to the problem of the separation of pairs of fluid elements. We have measured this separation rate in an intensely turbulent laboratory flow and have found, in quantitative agreement with the seminal predictions of Batchelor, that the initial separation of the pair plays an important role in the subsequent spreading of the fluid elements. These results have surprising consequences for the decay of concentration fluctuations and have applications to biological and chemical systems.

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); (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.

Compressibility in solar wind plasma turbulence

Incompressible magnetohydrodynamics is often assumed to describe solar wind turbulence. We use extended self-similarity to reveal scaling in the structure functions of density fluctuations in the solar wind. The obtained scaling is then compared with that found in the inertial range of quantities identified as passive scalars in other turbulent systems. We find that these are not coincident. This implies that either solar wind turbulence is compressible or that straightforward comparison of structure functions does not adequately capture its inertial range properties.

Intermittency of acceleration in isotropic turbulence

The intermittency of acceleration is investigated for isotropic turbulence using direct numerical simulation. Intermittently found acceleration of large magnitude always points towards the rotational axis of a vortex filament, indicating that the intermittency of acceleration is associated with the rotational motion of the vortices that causes centripetal acceleration, which is consistent with the reported result for the near-wall turbulence. Furthermore, investigation on movements of such vortex filaments provides some insights into the dynamics of local dissipation, enstrophy and acceleration. Strong dissipation partially covering the edge of a vortex filament shows weak correlation with enstrophy, while it is strongly correlated with acceleration.

Joint statistics of the Lagrangian acceleration and velocity in fully developed turbulence

We report experimental results on the joint statistics of the Lagrangian acceleration and velocity in highly turbulent flows. The acceleration was measured up to a microscale Reynolds number R(lambda)=690 using high speed silicon strip detectors from high energy physics. The acceleration variance was observed to be strongly dependent on the velocity, following a Heisenberg-Yaglom-like u(9/2) increase. However, the shape of the probability density functions of the acceleration component conditioned on the same component of the velocity when normalized by the acceleration variance was observed to be independent of velocity and to coincide with the unconditional probability density function of the acceleration components. This observation imposes a strong mathematical constraint on the possible functional form of the acceleration probability distribution function.

Acceleration statistics as measures of statistical persistence of streamlines in isotropic turbulence

We introduce the velocity Vs of stagnation points as a means to characterize and measure statistical persistence of streamlines. Using theoretical arguments, direct numerical simulations (DNS), and kinematic simulations (KS) of three-dimensional isotropic turbulence for different ratios of inner to outer length scales L/eta of the self-similar range, we show that a frame exists where the average Vs = 0 , that the rms values of acceleration, turbulent fluid velocity, and Vs are related by La'/u'2 approximately (V's/u')(L/eta)(2/3+q) , and that V's/u' approximately (L/eta)q with q = -1/3 in Kolmogorov turbulence, q = -1/6 in current DNS, and q = 0 in our KS. The statistical persistence hypothesis is closely related to the Tennekes sweeping hypothesis.

Three-dimensional 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 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.

Conditional Lagrangian acceleration statistics in turbulent flows with Gaussian-distributed velocities

The random intensity of noise approach to the one-dimensional Laval-Dubrulle-Nazarenko-type model having deductive support from the three-dimensional Navier-Stokes equation is used to describe Lagrangian acceleration statistics of a fluid particle in developed turbulent flows. Intensity of additive noise and cross correlation between multiplicative and additive noises entering a nonlinear Langevin equation are assumed to depend on random velocity fluctuations in an exponential way. We use an exact analytic result for the acceleration probability density function obtained as a stationary solution of the associated Fokker-Planck equation. We give a complete quantitative description of the available experimental data on conditional and unconditional acceleration statistics within the framework of a single model with a single set of fit parameters. The acceleration distribution and variance conditioned on Lagrangian velocity fluctuations and the marginal distribution calculated by using independent Gaussian velocity statistics are found to be in a good agreement with the recent high-Reynolds-number Lagrangian experimental data. The fitted conditional mean acceleration is very small, that is, in agreement with direct numerical simulations, and increases for higher velocities but it departs from the experimental data, which exhibit anisotropy of the studied flow.

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.

Anisotropy of acceleration in turbulent flows

Third-order Lagrangian stochastic models for the evolution of fluid-particle hyperaccelerations (material derivatives of Lagrangian accelerations) are shown to account naturally for the anisotropy of acceleration variances in low-Reynolds-number turbulent flows and for their dependency upon the energy-containing scales of motion. Model predictions are shown to be in close accord with the results of direct numerical simulations for a turbulent channel flow and with previously acquired simulation data for a homogeneous turbulent shear flow.

Varieties of dynamic multiscaling in fluid turbulence

We show that different ways of extracting time scales from time-dependent velocity structure functions lead to different dynamic-multiscaling exponents in fluid turbulence. These exponents are related to equal-time multiscaling exponents by different classes of bridge relations, which we derive. We check this explicitly by detailed numerical simulations of the Gledzer-Ohkitani-Yamada shell model for fluid turbulence. Our results can be generalized to any system in which both equal-time and time-dependent structure functions show multiscaling.

Intermittent nature of acceleration in near wall turbulence

Using direct numerical simulation of a fully developed turbulent channel flow, we investigate the behavior of acceleration near a solid wall. We find that acceleration near the wall is highly intermittent and the intermittency is in large part associated with the near wall organized coherent turbulence structures. We also find that acceleration of large magnitude is mostly directed towards the rotation axis of the coherent vortical structures, indicating that the source of the intermittent acceleration is the rotational motion associated with the vortices that causes centripetal acceleration.

Dispersion in the enstrophy cascade of two-dimensional decaying grid turbulence

The use of vertically flowing soap films allows one to obtain decaying two-dimensional turbulence with an enstrophy cascade range. Here we use this property to study the dispersion of a fine column of slightly heated liquid entering the turbulent flow. The width of this column increases with time in an exponential manner consistent with theoretical predictions for the average dispersion of particle pairs despite the multiparticle nature of the dispersion studied. Other features such as Gaussian mean profiles of the temperature across the channel width are also evidenced.

Influence of Eulerian and Lagrangian scales on the relative dispersion properties in Lagrangian stochastic models of turbulence

The influence of Eulerian and Lagrangian scales on the turbulent relative dispersion is investigated through a three-dimensional Eulerian consistent Lagrangian stochastic model. As a general property of this class of models, it is found to depend solely on a parameter beta based on the Kolmogorov constants C(K) and C0. This parameter represents the ratio between the Lagrangian and Eulerian scales and is related to the intrinsic inhomogeneity of the relative dispersion process. In particular, the quantity g*=g/C(0) (where g is the Richardson constant) and the temporal extension of the t(3) regime are found to be strongly dependent on the value adopted for beta.

One-dimensional Langevin models of fluid particle acceleration in developed turbulence

We make a comparative analysis of some recent one-dimensional Langevin models of the acceleration of a Lagrangian fluid particle in developed turbulent flow. The class of models characterized by random intensities of noises (RIN models) provides a fit to the recent experimental data on the acceleration statistics. We review the model by Laval, Dubrulle, and Nazarenko (LDN) formulated in terms of temporal velocity derivative in the rapid distortion theory approach, and propose its extension due to the RIN framework. The fit of the contribution to fourth-order moment of the acceleration is found to be better than in the other stochastic models. We study the acceleration probability density function conditional on velocity fluctuations implied by the RIN approach to the LDN-type model. The shapes of the conditional distributions and the conditional acceleration variance have been found in a good agreement with the recent experimental data by Mordant, Crawford, and Bodenschatz [Physica D (to be published), e-print physics/0303003].