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.
The notion of helical distributed chaos has been used for the description of the spatio-temporal dynamics of the passive scalar tracers from the atmospheric surface layer up to the mesosphere (at different stability conditions and different latitudes). Point, linear and distributed sources and sinks with different types of artificial and natural trace-gases (ozone, carbon dioxide, etc.), and aerosols have been studied. Related properties of the solar radiation transmittance in the cloudy atmosphere have been also briefly discussed as well as analogous properties of the tracers in Jupiter's atm…
The energy and flux budget (EFB) closure theory for a passive scalar (non-buoyant and non-inertial particles or gaseous admixtures) is developed for stably stratified turbulence. The physical background of the EFB turbulence closures is based on the budget equations for the turbulent kinetic and potential energies and turbulent fluxes of momentum and buoyancy, as well as the turbulent flux of particles. The EFB turbulence closure is designed for stratified geophysical flows from neutral to very stable stratification and it implies that turbulence is maintained by the velocity shear at any stra…
Spatio-temporal deterministic chaos at small Taylor-Reynolds numbers $Re_λ \lesssim 40$ and distributed chaos at turbulent $Re_λ \gtrsim 40$ in passive scalar dynamics have been studied using results of direct numerical simulations of homogeneous incompressible flows (with and without mean gradient of the passive scalar) for $8 \leq Re_λ < 700$ and of a reacting turbulent mixing layer. It is shown that the deterministic chaos in the passive scalar fluctuations at the small $Re_λ$ is characterized by exponential spatial (wavenumber) spectrum: $E(k) \propto \exp-(k/k_c)$, whereas the distributed…
We establish an hitherto hidden connection between zero modes and instantons in the context of the Kraichanan model for passive scalar turbulent advection, that relies on the hypothesis that the production of strong gradients of the scalar is associated with Bose-like condensation of Lagrangian particles. It opens the way to the computation of scaling exponents of the N-th order structure functions of the scalar by techniques borrowed from many-body theory. To lowest order of approximation, scaling exponents are found to increase asymptotically as log N in two dimensions.
In this paper we present an extension of the \emph{Recent Fluid Deformation (RFD)} closure introduced by Chevillard and Meneveau (2006) which was developed for modeling the time evolution of Lagrangian fluctuations in incompressible Navier-Stokes turbulence. We apply the RFD closure to study the evolution of magnetic and passive scalar fluctuations. This comparison is especially interesting since the stretching term for the magnetic field and for the gradient of the passive scalar are similar but differ by a sign such that the effect of stretching and compression by the turbulent velocity fiel…
We develop a mean-field theory of compressibility effects in turbulent magnetohydrodynamics and passive scalar transport using the quasi-linear approximation and the spectral $τ$-approach. We find that compressibility decreases the $α$ effect and the turbulent magnetic diffusivity both at small and large magnetic Reynolds numbers, Rm. Similarly, compressibility decreases the turbulent diffusivity for passive scalars both at small and large Péclet numbers, Pe. On the other hand, compressibility does not affect the effective pumping velocity of the magnetic field for large Rm, but it decreases i…
Passive scalar mixing, produced by Lagrangian chaos generated a) by quasi-periodic (integrable) motion of three quasi-point vortices and b) by chaotic motion of three and six quasi-point vortices, has been studied and compared with turbulent mixing of passive scalar in 2D and 3D steady isotropic homogeneous turbulence and in turbulent wakes behind grid and behind cylinder. Results of numerical and laboratory experiments have been used and effective diffusivity approximation as well as distributed chaos approach have been applied to this problem.
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.
A closure theory is developed for inhomogeneous turbulent flow, which enables a systematic derivation of the turbulence constitutive relations without relying on any empirical parameters. Renormalized-perturbation approximation is performed in the convective coordinate frame based on the mean flow, successfully incorporating the convective integration in generally covariant manner.
We use direct numerical simulations to compute turbulent transport coefficients for passive scalars in turbulent rotating flows. Effective diffusion coefficients in the directions parallel and perpendicular to the rotations axis are obtained by studying the diffusion of an imposed initial profile for the passive scalar, and calculated by measuring the scalar average concentration and average spatial flux as a function of time. The Rossby and Schmidt numbers are varied to quantify their effect on the effective diffusion. It is find that rotation reduces scalar diffusivity in the perpendicular d…
We outline a statistical theory of turbulence based on the Lagrangian formulation of fluid motion. We derive a hierarchy of evolution equations for Lagrangian N-point probability distributions as well as a functional equation for a suitably defined probability functional which is the analog of Hopf's functional equation. Furthermore, we adress the derivation of a generalized Fokker-Plank equation for the joint velocity - position probability density of N fluid particles.
In this paper, we employ Lagrangian coherent structures (LCSs) theory for the three dimensional vortex eduction and investigate the effect of large-scale vortical structures on the turbulent/non-turbulent interface (TNTI) and entrainment of a gravity current. The gravity current is realized experimentally and different levels of stratification are examined. For flow measurements, we use a multivolume three-dimensional particle tracking velocimetry technique. To identify vortical LCSs (VLCSs), a fully automated 3D extraction algorithm for multiple flow structures based on the so-called Lagrangi…
We present Lagrangian one-particle statistics from the Risoe PTV experiment of a turbulent flow. We estimate the Lagrangian Kolmogorov constant $C_0$ and find that it is affected by the large scale inhomogeneities of the flow. The pdf of temporal velocity increments are highly non-Gaussian for small times which we interpret as a consequence of intermittency. Using Extended Self-Similarity we manage to quantify the intermittency and find that the deviations from Kolmogorov 1941 similarity scaling is larger in the Lagrangian framework than in the Eulerian. Through the multifractal model we calcu…
We investigate experimentally the statistical properties of active and passive scalar fields in turbulent Rayleigh-Bénard convection in water, at $Ra\sim10^{10}$. Both the local concentration of fluorescence dye and the local temperature are measured near the sidewall of a rectangular cell. It is found that, although they are advected by the same turbulent flow, the two scalars distribute differently. This difference is twofold, i.e. both the quantities themselves and their small-scale increments have different distributions. Our results show that there is a certain buoyant scale based on time…
Chaotic and turbulent dispersion of passive heavy inertial particles in homogeneous two-dimensional turbulence with Ekman drag has been studied using notions of the effective diffusivity and distributed chaos. Results of recent direct numerical simulations have been used for this purpose. Effect of the Stokes number value on the applicability of these notions to the dispersion of passive heavy inertial particles has been briefly discussed.
We develop a passive control strategy for suppressing thermoacoustic instability in a bluff-body stabilized premixed turbulent combustor. When the equivalence ratio is varied, there is a transition from combustion noise to thermoacoustic instability via intermittency in the combustor. We perform simultaneous acoustic pressure, 2D-PIV, and CH$^*$ chemiluminescence measurements to capture the pressure fluctuations, the velocity field, and the heat release rate (HRR) field during the transition. We measure the spatial distribution of the amplitude of turbulent velocity at the acoustic frequency, …
Turbulent Rayleigh-Benard 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 Gamma 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…
The statistical properties of the Lagrangian acceleration vector of passive tracers in statistically-steady rotating turbulence is studied by Particle Tracking Velocimetry. Direct effects of the background rotation are the suppression of high-acceleration events parallel to the (vertical) rotation axis, the enhancement of high-acceleration events for the horizontal acceleration, and the strong amplification of the auto-correlation of the acceleration component perpendicular to both the rotation vector Ω and local velocity vector u. The auto-correlation of the acceleration component in the plan…
A temporal complex network-based approach is proposed as a novel formulation to investigate turbulent mixing from a Lagrangian viewpoint. By exploiting a spatial proximity criterion, the dynamics of a set of fluid particles is geometrized into a time-varying weighted network. Specifically, a numerically solved turbulent channel flow is employed as an exemplifying case. We show that the time-varying network is able to clearly describe the particle swarm dynamics, in a parametrically robust and computationally inexpensive way. The network formalism enables to straightforwardly identify transient…
We investigate the Lagrangian statistics of three-dimensional rotating turbulent flows through direct numerical simulations. We find that the emergence of coherent vortical structures because of the Coriolis force leads to a suppression of the "flight-crash" events reported by Xu, et al. [Proc. Natl. Acad. Sci. (U.S.A) 111, 7558 (2014)]. We perform systematic studies to trace the origins of this suppression in the emergent geometry of the flow and show why such a Lagrangian measure of irreversibility may fail in the presence of rotation.
Passive scalar transport in turbulent channel flow subject to spanwise system rotation is studied by direct numerical simulations. The Reynolds number $Re = U_b h/ν$ is fixed at $20\,000$ and the rotation number $Ro = 2 Ωh/U_b$ is varied from 0 to 1.2, where $U_b$ is the bulk mean velocity, $h$ the half channel gap width and $Ω$ the rotation rate. The scalar value is constant but different at the two walls, leading to steady scalar transport across the channel. The rotation causes an unstable channel side with relatively strong turbulence and turbulent scalar transport, and a stable channel si…
Direct numerical simulation data show that the variance of the coupling term in passive scalar advection by a random velocity field is smaller than it would be if the velocity and scalar fields were statistically independent. This effect is analogous to the "depression of nonlinearity" in hydrodynamic turbulence. We show that the trends observed in the numerical data are qualitatively consistent with the predictions of closure theories related to Kraichnan's direct interaction approximation. The phenomenon is demonstrated over a range of Prandtl numbers. In the inertial-convective range the de…
In the context of instanton method for stochastic system this paper purposes a modification of the arclength parametrization of the Hamilton's equations allowing for an arbitrary instanton speed. The main results of the paper are: (i) it generalizes the parametrized Hamilton's equations to any speed required. (ii) corrects the parametric action on the occasion that the Hamiltonian is small but finite and how it adjusts to the probability density function (pdf). (iii) Improves instanton approximation to pdf by noise and propagator renormalization. As an application of the above set up we predic…
We investigate the utility of the convex hull of many Lagrangian tracers to analyze transport properties of turbulent flows with different anisotropy. In direct numerical simulations of statistically homogeneous and stationary Navier-Stokes turbulence, neutral fluid Boussinesq convection, and MHD Boussinesq convection a comparison with Lagrangian pair dispersion shows that convex hull statistics capture the asymptotic dispersive behavior of a large group of passive tracer particles. Moreover, convex hull analysis provides additional information on the sub-ensemble of tracers that on average di…
Lagrangian acceleration statistics in a fully developed turbulent channel flow at $Re_τ= 1440$ are investigated, based on tracer particle tracking in experiments and direct numerical simulations. The evolution with wall distance of the Lagrangian velocity and acceleration time scales is analyzed. Dependency between acceleration components in the near-wall region is described using cross-correlations and joint probability density functions. The strong streamwise coherent vortices typical of wall-bounded turbulent flows are shown to have a significant impact on the dynamics. This results in a st…
Passive scalars in turbulent channel flows are investigated as canonical problem for heat and mass transfer in turbulent boundary-layer flows. The one-dimensional turbulence model is used to numerically investigate the Schmidt and Reynolds number dependence of the scalar transfer to a wall due to fluctuating wall-normal transport. First, the model is calibrated for low-order velocity statistics. After that, we keep the model parameters fixed and investigate low-order passive scalar statistics for a relevant Schmidt and Reynolds number range. We show that the model consistently predicts the bou…
The advection and mixing of a scalar quantity by fluid flow is an important problem in engineering and natural sciences. If the fluid is turbulent, the statistics of the passive scalar exhibit complex behavior. This paper is concerned with two Lagrangian scalar turbulence models based on the recent fluid deformation model that can be shown to reproduce the statistics of passive scalar turbulence for a range of Reynolds numbers. For these models, we demonstrate how events of extreme passive scalar gradients can be recovered by computing the instanton, i.e., the saddle-point configuration of the…
Self-consistent closure theory for passive-scalar turbulence has been developed on the basis of the Hessian of the scalar field. As a primitive indicator of spatial structure of the scalar, we employ the Hessian into the core of the theory to properly characterize the time scale intrinsic to the scalar field itself. The resultant closure model is now endowed with several realistic features, i.e. the scale-locality of the interscale interaction, the detailed conservation, and the memory-fading effect. Applying the current theory to the inertial-convective range eventually leads to self-consiste…
We study the influence of the energy spectrum on the extent of the cascade range of a passive tracer in turbulent flows. The interesting cases are when there are two different spectra over the potential range of the tracer cascade (in 2D when the tracer forcing is in the inverse energy cascade range, and in 3D when the Schmidt number Sc is large). The extent of the tracer cascade range is then limited by the width of the range for the shallower of the two energy spectra. Nevertheless, we show that in dimension $d=2,3$ the tracer cascade range extends (up to a logarithm) to $κ_{d\text{D}}^{p}$,…
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 (PDF) 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 accelera…
We investigate the response of large inertial particle to turbulent fluctuations in a inhomogeneous and anisotropic flow. We conduct a Lagrangian study using particles both heavier and lighter than the surrounding fluid, and whose diameters are comparable to the flow integral scale. Both velocity and acceleration correlation functions are analyzed to compute the Lagrangian integral time and the acceleration time scale of such particles. The knowledge of how size and density affect these time scales is crucial in understanding partical dynamics and may permit stochastic process modelization usi…
The effects of passive scalar anisotropy on subgrid-scale (SGS) physics and modeling for Large-Eddy Simulations are studied experimentally. Measurements are performed across a moderate Reynolds number wake flow generated by a heated cylinder, using an array of four X-wire and four cold-wire probes. By varying the separation distance among probes in the array, we obtain filtered and subgrid quantities at three different filter sizes. We compute several terms that comprise the subgrid dissipation tensor of kinetic energy and scalar-variance and test for isotropic behavior, as a function of filte…
The computational cost of fluid simulations increases rapidly with grid resolution. This has given a hard limit on the ability of simulations to accurately resolve small scale features of complex flows. Here we use a machine learning approach to learn a numerical discretization that retains high accuracy even when the solution is under-resolved with classical methods. We apply this approach to passive scalar advection in a two-dimensional turbulent flow. The method maintains the same accuracy as traditional high-order flux-limited advection solvers, while using 4x lower grid resolution in each…
The Lagrangian point of view is adopted to study turbulent premixed combustion. The evolution of the volume fraction of combustion products is established by the Reynolds transport theorem. It emerges that the burned-mass fraction is led by the turbulent particle motion, by the flame front velocity, and by the mean curvature of the flame front. A physical requirement connecting particle turbulent dispersion and flame front velocity is obtained from equating the expansion rates of the flame front progression and of the unburned particles spread. The resulting description compares favorably with…
Three-dimensional turbulence simulations are used to show that the turbulent root mean square velocity is an upper bound of the speed of turbulent diffusion. There is a close analogy to magnetic diffusion where the maximum diffusion speed is the speed of light. Mathematically, this is caused by the inclusion of the Faraday displacement current which ensures that causality is obeyed. In turbulent diffusion, a term similar to the displacement current emerges quite naturally when the minimal tau approximation is used. Simulations confirm the presence of such a term and give a quantitative measure…
A Lagrangian experimental study of an axisymmetric turbulent water jet is performed to investigate the highly anisotropic and inhomogeneous flow field. The measurements were conducted within a Lagrangian exploration module, an icosahedron apparatus, to facilitate optical access of three cameras. The stereoscopic particle tracking velocimetry results in three component tracks of position, velocity and acceleration of the tracer particles within the vertically-oriented jet with a Taylor-based Reynolds number $\mathcal R_λ\simeq 230$. Analysis is performed at seven locations from 15 diameters up …
We report joint Lagrangian velocity and temperature measurements in turbulent thermal convection. Measurements are performed using an improved version (extended autonomy) of the neutrally-buoyant instrumented particle that was used by to performed experiments in a parallelepipedic Rayleigh-Benard cell. The temperature signal is obtained from a RFtransmitter. Simultaneously, we determine particle's position and velocity with one camera, which grants access to the Lagrangian heat flux. Due to the extended autonomy of the present particle, we obtain well converged temperature and velocity statist…
Heavy inertial particles transported by a turbulent flow are shown to concentrate in the regions where an advected passive scalar, such as temperature, displays very strong front-like discontinuities. This novel effect is responsible for extremely high levels of fluctuations for the passive field sampled by the particles that impacts the heat fluxes exchanged between the particles and the surrounding fluid. Instantaneous and averaged heat fluxes are shown to follow strongly intermittent statistics and anomalous scaling laws.
Spatial regions that do not mix effectively with their surroundings and thus contribute less to the heat transport in fully turbulent three-dimensional Rayleigh-Bénard flows are identified by Lagrangian trajectories that stay together for a longer time. These trajectories probe Lagrangian coherent sets (CS) which we investigate here in direct numerical simulations in convection cells with square cross section of aspect ratio $Γ= 16$, Rayleigh number $Ra = 10^{5}$, and Prandtl numbers $Pr = 0.1, 0.7$ and $7$. The analysis is based on $N=524,288$ Lagrangian tracer particles which are advected in…
Conditional statistics of homogeneous isotropic turbulent flow is investigated by means of high-Reynolds number direct numerical simulations performed with $2048^3$ collocation points. Eulerian as well as Lagrangian velocity increment statistics under several conditions are analyzed and compared. In agreement with experimental data longitudinal probability density functions $P(δ^{||}_l u|ε_l)$ conditioned on a scale-averaged energy dissipation rate are close to Gaussian distributions over all scales within the inertial range of scales. Also transverse increments conditioned on either the dissi…
We analyze large-scale patterns in three-dimensional turbulent convection in a horizontally extended square convection cell by Lagrangian particle trajectories calculated in direct numerical simulations. A simulation run at a Prandtl number Pr $=0.7$, a Rayleigh number Ra $=10^5$, and an aspect ratio $Γ=16$ is therefore considered. These large-scale structures, which are denoted as turbulent superstructures of convection, are detected by the spectrum of the graph Laplacian matrix. Our investigation, which follows Hadjighasem {\it et al.}, Phys. Rev. E {\bf 93}, 063107 (2016), builds a weighted…
We show that the probability densities af accelerations of Lagrangian test particles in turbulent flows as measured by Bodenschatz et al. [Nature 409, 1017 (2001)] are in excellent agreement with the predictions of a stochastic model introduced in [C. Beck, PRL 87, 180601 (2001)] if the fluctuating friction parameter is assumed to be log-normally distributed. In a generalized statistical mechanics setting, this corresponds to a superstatistics of log-normal type. We analytically evaluate all hyperflatnes factors for this model and obtain a flatness prediction in good agreement with the experim…
Coherent circulation rolls and their relevance for the turbulent heat transfer in a two-dimensional Rayleigh--Bénard convection model are analyzed. The flow is in a closed cell of aspect ratio four at a Rayleigh number ${\rm Ra}=10^6$ and at a Prandtl number ${\rm Pr}=10$. Three different Lagrangian analysis techniques based on graph Laplacians -- distance spectral trajectory clustering, time-averaged diffusion maps and finite-element based dynamic Laplacian discretization -- are used to monitor the turbulent fields along trajectories of massless Lagrangian particles in the evolving turbulent …
The Lagrangian approach is natural to study issues of turbulent dispersion and mixing. We propose in this work a general Lagrangian stochastic model including velocity and acceleration as dynamical variables for inhomogeneous turbulent flows. The model takes the form of a diffusion process and the coefficients of the model are determined via Kolmogorov theory and the requirement of consistency with the velocity-based models. It is shown that the present model generalises both the acceleration-based models for homogeneous flows and the generalised Langevin models for the velocity. The resulting…
We study how helicity affects the spectrum of a passive scalar in rotating turbulent flows, using numerical simulations of turbulent flows with or without rotation, and with or without injection of helicity. Scaling laws for energy and passive scalar spectra in the direction perpendicular to the rotation axis differ in rotating helical flows from the ones found in the non-helical case, with the spectrum of passive scalar variance in the former case being shallower than in the latter. A simple phenomenological model that links the effects of helicity on the energy spectrum with the passive scal…
In heat transfer augmenting methods such as radial fins, the heat transfer enhancement commonly leads to the drag force increment. In the present paper, slots are inserted over the fins to simultaneously reduce the drag coefficient. Turbulent convection heat transfer around a cylinder, as well as oscillating bundle of tubes including the slotted radial fins have been investigated. The governing equations are solved in two-dimension utilizing OpenFOAM software based on k-ω SST closure model. The cases with various slot location, slot width, the number of the slots, the fin height, and oscillati…
The Eulerian-Lagrangian approach based on Large-Eddy Simulation (LES) is one of the most promising and viable numerical tools to study turbulent dispersed flows when the computational cost of Direct Numerical Simulation (DNS) becomes too expensive. The applicability of this approach is however limited if the effects of the Sub-Grid Scales (SGS) of the flow on particle dynamics are neglected. In this paper, we propose to take these effects into account by means of a Lagrangian stochastic SGS model for the equations of particle motion. The model extends to particle-laden flows the velocity-filte…
We investigate the ability of 4D Particle Tracking Velocimetry measurements at high particle density to explore intermittency and irreversibility in a turbulent swirling flow at various Reynolds numbers. For this, we devise suitable tools to remove the experimental noise, and compute the statistics of both Lagrangian velocity increments and wavelet coefficients of the Lagrangian power (the time derivative of the kinetic energy along a trajectory). We show that the signature of noise is strongest on short trajectories, and results in deviations from the regularity condition at small time scales…
High-speed stereo PIV-measurements have been performed in a turbulent boundary layer at Re$_θ$ of 9800 in order to elucidate the coherent structures. Snapshot proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) are used to visualize the flow structure depending on the turbulent kinetic energy and frequency content. The first six POD and DMD modes show the largest and the lowest amount of energy and frequency, respectively. Lagrangian coherent structure (LCS) based on the algorithm developed using the variational theory is also applied to track the flow via attracting and…
