Preferential concentration of heavy particles in stably stratified turbulence

The effect of preferential concentration of heavy particles in a homogeneous stably stratified turbulent flow is studied by means of direct numerical simulations. Particle distributions show different clustering patterns in horizontal and vertical directions, thereby representing the anisotropy of the flow. Preferential concentration in stably stratified turbulence can be quantified using 2D and 3D radial distribution functions and the correlation dimension D2. With increasing stratification strength, the effect of preferential concentration decreases. Furthermore, it is found that in stably stratified turbulence preferential accumulation is enhanced when gravitational forces act on heavy particles.     

Numerical investigation of self-similar unstably stratified homogeneous turbulence

New numerical results concerning unstably stratified homogeneous turbulence are presented. The system of equations considered gives the dynamics of homogeneous incompressible binary mixtures submitted to a gravity field in the low Atwood number limit (Boussinesq approximation). It allows to gain insight into several characteristics relevant to buoyancy driven turbulent mixing, such as unsteadiness and anisotropy. In this work, the dependency of the asymptotic self-similar states on different dissipation processes is extensively explored. The resulting states are shown to agree with recent theoretical predictions based on a large scale dynamics analysis.     

Particle subgrid scale modelling in large-eddy simulations of particle-laden turbulence

This study is concerned with particle subgrid scale (SGS) modelling in large-eddy simulations (LESs) of particle-laden turbulence. Although many particle-laden LES studies have neglected the effect of the SGS on the particles, several particle SGS models have been proposed in the literature. In this research, the approximate deconvolution method (ADM) and the stochastic models of Fukagata et al. (Dynamics of Brownian particles in a turbulent channel flow, Heat Mass Transf. 40 (2004), 715–726) Shotorban and Mashayek (A stochastic model for particle motion in large-eddy simulation, J. Turbul. 7 (2006), 1–13) and Berrouk et al. (Stochastic modelling of inertial particle dispersion by subgrid motion for LES of high Reynolds number pipe flow, J. Turbul. 8 (2007), pp. 1–20) are analysed. The particle SGS models are assessed using both a priori and a posteriori simulations of inertial particles in a periodic box of decaying, homogeneous and isotropic turbulence with an initial Reynolds number of Re_λ = 74. The model results are compared with particle statistics from a direct numerical simulation (DNS). Particles with a large range of Stokes numbers are tested using various filter sizes and stochastic model constant values. Simulations with and without gravity are performed to evaluate the ability of the models to account for the crossing trajectory and continuity effects. The results show that ADM improves results but is only capable of recovering a portion of the SGS turbulent kinetic energy. Conversely, the stochastic models are able to recover sufficient SGS energy, but show a large range of results dependent on the Stokes number and filter size. The stochastic models generally perform best at small Stokes numbers, but are unable to predict preferential concentration.     

Adaptation of mesoscale turbulence parameterisation schemes as RANS closures for ABL simulations

The present study presents different k-ε turbulence closures for atmospheric boundary layer flows using computational fluid dynamics (CFD) simulations that are consistent with inflow conditions from numerical weather prediction (NWP) simulations. Eight different mesoscale turbulence parameterisation schemes of the Weather Research and Forecasting (WRF) model are covered. To ensure consistency between the NWP and CFD simulations, different closure coefficients of the k ? ε turbulence model for each NWP scheme are proposed. This is achieved by combining production–dissipation closure coefficient relationships based on the Monin–Obukhov similarity theory and the formulation based on the Coriolis parameter proposed by Detering and Etling. The proposed methodology has been implemented in the open source CFD toolbox OpenFOAM and is demonstrated at near-neutral stability conditions for the classical Askervein Hill case.     

Statistical models for spatial patterns of heavy particles in turbulence

The dynamics of heavy particles suspended in turbulent flows is of fundamental importance for a wide range of questions in astrophysics, atmospheric physics, oceanography, and technology. Laboratory experiments and numerical simulations have demonstrated that heavy particles respond in intricate ways to turbulent fluctuations of the carrying fluid: non-interacting particles may cluster together and form spatial patterns even though the fluid is incompressible, and the relative speeds of nearby particles can fluctuate strongly. Both phenomena depend sensitively on the parameters of the system. This parameter dependence is difficult to model from first principles since turbulence plays an essential role. Laboratory experiments are also very difficult, precisely since they must refer to a turbulent environment. But in recent years it has become clear that important aspects of the dynamics of heavy particles in turbulence can be understood in terms of statistical models where the turbulent fluctuations are approximated by Gaussian random functions with appropriate correlation functions. In this review, we summarise how such statistical-model calculations have led to a detailed understanding of the factors that determine heavy-particle dynamics in turbulence. We concentrate on spatial clustering of heavy particles in turbulence. This is an important question because spatial clustering affects the collision rate between the particles and thus the long-term fate of the system.     

Cumulative compressibility effects on slow reactive dynamics in turbulent flows

Reactions in turbulent flows, chemical reactions or combustion, are common. Typically reaction time scales are much shorter than turbulence timescales. In biological applications, as it is the case for bacterial and plankton populations living under the influence of currents in oceans and lakes, the typical lifetime can be long and thus can fall well within the inertial range of turbulence time scales. Under these conditions, turbulent transport interacts in a very complex way with the dynamics of growth and death of the individuals in the population. In the present paper, we quantitatively investigate the effect of the flow compressibility on the dynamics of populations. Small effective compressibility can be induced by several physical mechanisms, such as, e.g., by the density mismatch, by a small but finite size of microorganisms, and by gyrotaxis (an interaction between swimming and shear). We report, for the first time, how even a tiny effective compressibility can produce a dramatically large effect on global quantities like the carrying capacity of the ecosystem. We interpret our findings by means of a cumulative effect made possible by the long replication times of the organisms with respect to turbulence time scales. A statistical quantification of the fluctuations of population concentration is presented.     

Reassessment of the classical closures for scalar turbulence

In deducing the consequences of the Direct Interaction Approximation, Kraichnan was sometimes led to consider the properties of special classes of nonlinear interactions in degenerate triads in which one wavevector is very small. Such interactions can be described by simplified models closely related to elementary closures for homogeneous isotropic turbulence such as the Heisenberg and Leith models. These connections can be exploited to derive considerably improved versions of the Heisenberg and Leith models that are only slightly more complicated analytically. This paper applies this approach to derive some new simplified closure models for passive scalar advection and investigates the consistency of these models with fundamental properties of scalar turbulence. Whereas some properties, such as the existence of the Kolmogorov–Obukhov range and the existence of thermal equilibrium ensembles, follow the velocity case closely, phenomena special to the scalar case arise when the diffusive and viscous effects become important at different scales of motion. These include the Batchelor and Batchelor–Howells–Townsend ranges pertaining, respectively, to high and low molecular Schmidt number. We also consider the spectrum in the diffusive range that follows the Batchelor range. We conclude that improved elementary models can be made consistent with many nontrivial properties of scalar turbulence, but that such models have unavoidable limitations.     

Response of plasma turbulence against externally-controlled perturbations

A theory of the dynamic response of the turbulent plasma against the externally-controlled perturbations is reported. Based on Mori’s method [Prog. Theor. Phys. 33 423 (1965)], the nonlinear force is assumed to be separated into the memory function and the nonlinear fluctuating force. The former corresponds to the damping term, and the latter is categorized into the noise term. The response of the turbulent plasma against the externally-controlled source is formulated. The response kernel, which connects the externally-controlled source and the response of the turbulent field, is shown to have both the nonlocal property (in space) and the non-Markovian response (in time). A discussion is made on the nonlocal and non-Markovian response, including the case of disparate-scale interactions. A new method is proposed to observe experimentally the nonlocal interaction in the drift wave turbulence via the zonal flows.     

High-order generalisation of the diagnostic scaling for turbulent boundary layers

The diagnostic scaling concept, introduced for the streamwise turbulence intensity in wall-bounded turbulent flows (Alfredsson, Segalini and Örlü, Phys. Fluids 2011;23:041702), is here extended and generalised not only for the higher even-order central statistical moments, but also for the odd moments and thereby the probability density distribution of the streamwise velocity fluctuations. Turbulent boundary layer data up to a friction Reynolds number of 60,000 are employed and demonstrate the feasibility of the diagnostic scaling for the data throughout the logarithmic and wake regions. A comparison with the generalised logarithmic law for even-order moments by Meneveau and Marusic (J. Fluid Mech. 2013;719:R1) based on the attached-eddy hypothesis, is reported. The diagnostic plot provides an apparent Reynolds-number-independent scaling of the data, and is exploited to reveal the functional dependencies of the constants needed in the attached-eddy-based model. In particular, the invariance of the lowest order diagnostic scaling poses an intriguing incompatibility with the asymptotic constancy of the Townsend–Perry constant.     

Mixing of a passive scalar across a thin shearless layer: concentration of intermittency on the sides of the turbulent interface

The advection of a passive scalar through an initial flat interface separating two different isotropic decaying turbulent fields is investigated in two and three dimensions. Simulations have been performed for a range of Taylor’s microscale Reynolds numbers from 45 to 250 and for a Schmidt number equal to 1. Different to the case where the transport involves the momentum and kinetic energy only and one intermittency layer is formed in the low-turbulent energy side of the system, in the passive scalar concentration field two intermittent layers are observed to develop at the sides of the interface. The layers move normally to the interface in opposite directions. The dimensionality produces different time scaling of the passive scalar diffusion, which is much faster in the two-dimensional case. In two dimensions, the propagation of the intermittent layers exhibits a significant asymmetry with respect to the initial position of the interface and is deeper for the layer which moves towards the high kinetic energy side of the system. In three dimensions, the two intermittent layers propagate nearly symmetrically with respect the centre of the mixing region. During the temporal decay, inside the mixing, which is both inhomogeneous and anisotropic but devoid of a mean velocity shear, the passive scalar spectra are computed. In three dimensions, the exponent in the scaling range gets in time a value close to that of the kinetic energy spectrum of isotropic turbulence (?5/3). In two dimensions, instead the exponent settles down to a value that is about one-half of the corresponding isotropic case. By means of an analysis based on simple wavy perturbations of the interface we show that the formation of the double layer of intermittency is a dynamic general feature not specific to the turbulent transport. These results of our numerical study are discussed in the context of experimental results and numerical simulations.     

Average intensity of flattened Gaussian beam in non-Kolmogorov turbulence

Based on the extended Huygens-Fresnel principle and the first-order approximation of wave structure function, an analytical expression for the average intensity of flattened Gaussian beam (FGB) in non-Kolmogorov turbulence has been derived. The variations of normalized intensity with some parameters, such as wave coherence length, Fresnel number, waist width and the order of FGB are investigated in detail.     

Inertial clustering of particles in high-Reynolds-number turbulence

We report experimental evidence of spatial clustering of dense particles in homogenous, isotropic turbulence at high Reynolds numbers. The dissipation-scale clustering becomes stronger as the Stokes number increases and is found to exhibit similarity with respect to the droplet Stokes number over a range of experimental conditions (particle diameter and turbulent energy dissipation rate). These findings are in qualitative agreement with recent theoretical and computational studies of inertial particle clustering in turbulence. Because of the large Reynolds numbers a broad scaling range of particle clustering due to turbulent mixing is present, and the inertial clustering can clearly be distinguished from that due to mixing of fluid particles.     

Statistics of velocity gradients in wall-bounded shear flow turbulence

The statistical properties of velocity gradients in a wall-bounded turbulent channel flow are discussed on the basis of three-dimensional direct numerical simulations. Our analysis is concentrated on the trend of the statistical properties of the local enstrophy and the energy dissipation rate with increasing distance from the wall. We detect a sensitive dependence of the largest amplitudes of both fields (which correspond with the tail of the distribution) on the spectral resolution. The probability density functions of each single field as well as their joint distribution vary significantly with increasing distance from the wall. The largest fluctuations of the velocity gradients are found in the logarithmic layer. This is in agreement with recent experiments which observe a bursting of hairpin vortex packets into the logarithmic region.     

On mean flow universality of turbulent wall flows. I. High Reynolds number flow analysis

ABSTRACT

The universality and mathematical physical structure of wall-bounded turbulent flows is a topic of discussions over many decades. There is no agreement about questions like what is the physical mean flow structure, how universal is it, and how universal are theoretical concepts for local and global flow variations. These questions are addressed by using latest direct numerical simulation (DNS) data at moderate Reynolds numbers Re and experimental data up to extreme Re. The mean flow structure is explained by analytical models for three canonical wall-bounded turbulent flows (channel flow, pipe flow, and the zero-pressure gradient turbulent boundary layer). Thorough comparisons with DNS and experimental data provide support for the validity of models. Criteria for veritable physics derived from observations are suggested. It is shown that the models presented satisfy these criteria. A probabilistic interpretation of the mean flow structure shows that the physical constraints of equal entropies and equally likely mean velocity values in a region unaffected by boundary effects impose a universal log-law structure. The structure of wall-bounded turbulent flows is much more universal than previously expected. There is no discrepancy between local logarithmic velocity variations and global friction law and bulk velocity variations. Flow effects are limited to the minimum: the difference of having a bounded or unbounded domain, and the variation range of mean velocity values allowed by the geometry.     

A study on turbulence modulation via an analysis of turbulence anisotropy-invariants

We investigate the turbulence modulation by particles in a turbulent two-phase channel flow via an analysis of turbulence anisotropy-invariants. The fluid turbulence is calculated by a large eddy simulation with a point-force two-way coupling model and particles are tracked by the Lagrangian trajectory method. The channel turbulence follows the two-component turbulence state within the viscous sub-layer region and outside the region the turbulence tends to follow the right curve of the anisotropy-invariant....     

Understanding the sub-critical transition to turbulence in wall flows

In contrast with free shear flows presenting velocity profiles with inflection points which cascade to turbulence in a relatively mild way, wall bounded flows are deprived of (inertial) instability modes at low Reynolds numbers and become turbulent in a much wilder way, most often marked by the coexistence of laminar and turbulent domains at intermediate Reynolds numbers, well below the range where (viscous) instabilities can show up. There can even be no unstable mode at all, as for plane Couette flow (pCf) or for Poiseuille pipe flow (Ppf) that are currently the subject of intense research. Though the mechanisms involved in the transition to turbulence in wall flows are now better understood, statistical properties of the transition itself are yet unsatisfactorily assessed. A widely accepted interpretation rests on non-trivial solutions of the Navier-Stokes equations in the form of unstable travelling waves and on transient chaotic states associated to chaotic repellors. Whether these concepts typical of the theory of temporal chaos are really appropriate is yet unclear owing to the fact that, strictly speaking, they apply when confinement in physical space is effective while the physical systems considered are rather extended in at least one space direction, so that spatiotemporal behaviour cannot be ruled out in the transitional regime. The case of pCf will be examined in this perspective through numerical simulations of a model with reduced cross-stream (y) dependence, focusing on the in-plane (x, z) space dependence of a few velocity amplitudes. In the large aspect-ratio limit, the transition to turbulence takes place via spatiotemporal intermittency and we shall attempt to make a connection with the theory of first-order (thermodynamic) phase transitions, as suggested long ago by Pomeau.      

双侧进气突扩燃烧室中三维湍流有施回流两相流动的数值模拟

双侧进气突扩燃烧室中三维湍流有施回流两相流动的数值模拟周力行，林文漪，廖昌明（清华大学工程力学系北京１０００８４）关键词：湍流两相流，数值模拟为提高整体式冲压发动机双侧进气突扩燃烧室火焰稳定能力，我们提出了进气管内装设有切向导角的中心管。流场显示及Ｌ...     

What do we know about self-similarity in fluid turbulence?

The evidence is reviewed on the statistical behavior of the small-scale fluctuations in high-Reynolds-number fluid turbulence. The qualitative phenomeno-logical information is summarized and the predictions of the 1941 Kolmogorov theory are reviewed. Then direct numerical simulation and its role in suggesting dynamical mechanisms are briefly discussed. Finally, the evidence on the multifractal structure of the dissipation field is reviewed. It is concluded that the experimental evidence for some kind of dynamical self-similarity is strong, but that there has been essentially no progress in fundamental theoretical understanding of the underlying mechanisms.