Non-Gaussian scalar statistics in homogeneous turbulence

1996 ◽  
Vol 313 ◽  
pp. 241-282 ◽  
Author(s):  
F. A. Jaberi ◽  
R. S. Miller ◽  
C. K. Madnia ◽  
P. Givi
Keyword(s):  
Turbulent Flows ◽  
Initial Conditions ◽  
Single Point ◽  
Passive Scalar ◽  
Small Scale ◽  
Velocity Fluctuations ◽  
Spatial Derivatives ◽  
Linear Eddy Model ◽  
Non Gaussian ◽  
Scalar Amplitude

Results are presented of numerical simulations of passive scalar mixing in homogeneous, incompressible turbulent flows. These results are generated via the Linear Eddy Model (LEM) and Direct Numerical Simulation (DNS) of turbulent flows under a variety of different conditions. The nature of mixing and its response to the turbulence field is examined and the single-point probability density function (p.d.f.) of the scalar amplitude and the p.d.f.s of the scalar spatial-derivatives are constructed. It is shown that both Gaussian and exponential scalar p.d.f.s emerge depending on the parameters of the simulations and the initial conditions of the scalar field. Aided by the analyses of data, several reasons are identified for the non-Gaussian behaviour of the scalar amplitude. In particular, two mechanisms are identified for causing exponential p.d.f.s: (i) a non-uniform action of advection on the large and the small scalar scales, (ii) the nonlinear interaction of the scalar and the velocity fluctuations at small scales. In the absence of a constant non-zero mean scalar gradient, the behaviour of the scalar p.d.f. is very sensitive to the initial conditions. In the presence of this gradient, an exponential p.d.f. is not sustained regardless of initial conditions. The numerical results pertaining to the small-scale intermittency (non-Gaussian scalar derivatives) are in accord with laboratory experimental results. The statistics of the scalar derivatives and those of the velocity-scalar fluctuations are also in accord with laboratory measured results.

Asymptotic Effect of Initial and Upstream Conditions on Turbulence

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
William K. George
Keyword(s):  
New York ◽  
Turbulent Flows ◽  
Coherent Structures ◽  
Large Scale ◽  
Initial Conditions ◽  
Single Point ◽  
Building Blocks ◽  
The Self ◽  
Asymptotic Independence ◽  
Small Scale

More than two decades ago the first strong experimental results appeared suggesting that turbulent flows might not be asymptotically independent of their initial (or upstream) conditions (Wygnanski et al., 1986, “On the Large-Scale Structures in Two-Dimensional Smalldeficit, Turbulent Wakes,” J. Fluid Mech., 168, pp. 31–71). And shortly thereafter the first theoretical explanations were offered as to why we came to believe something about turbulence that might not be true (George, 1989, “The Self-Preservation of Turbulent Flows and its Relation to Initial Conditions and Coherent Structures,” Advances in Turbulence, W. George and R. Arndt, eds., Hemisphere, New York, pp. 1–41). These were contrary to popular belief. It was recognized immediately that if turbulence was indeed asymptotically independent of its initial conditions, it meant that there could be no universal single point model for turbulence (George, 1989, “The Self-Preservation of Turbulent Flows and its Relation to Initial Conditions and Coherent Structures,” Advances in Turbulence, W. George and R. Arndt, eds., Hemisphere, New York, pp. 1–41; Taulbee, 1989, “Reynolds Stress Models Applied to Turbulent Jets,” Advances in Turbulence, W. George and R. Arndt, eds., Hemisphere, New York, pp. 29–73) certainly consistent with experience, but even so not easy to accept for the turbulence community. Even now the ideas of asymptotic independence still dominate most texts and teaching of turbulence. This paper reviews the substantial additional evidence - experimental, numerical and theoretical - for the asymptotic effect of initial and upstream conditions that has accumulated over the past 25 years. Also reviewed is evidence that the Kolmogorov theory for small scale turbulence is not as general as previously believed. Emphasis has been placed on the canonical turbulent flows (especially wakes, jets, and homogeneous decaying turbulence), which have been the traditional building blocks for our understanding. Some of the important outstanding issues are discussed; and implications for the future of turbulence modeling and research, especially LES and turbulence control, are also considered.

scholarly journals Velocity and temperature derivatives in high-Reynolds-number turbulent flows in the atmospheric surface layer. Part 2. Accelerations and related matters

2007 ◽  
Vol 589 ◽  
pp. 83-102 ◽  
Author(s):  
G. GULITSKI ◽  
M. KHOLMYANSKY ◽  
W. KINZELBACH ◽  
B. LÜTHI ◽  
A. TSINOBER ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Turbulent Flows ◽  
Atmospheric Surface Layer ◽  
Field Experiments ◽  
Small Scale ◽  
Velocity Fluctuations ◽  
First Results ◽  
Taylor Hypothesis ◽  
Spatial Derivatives ◽  
High Reynolds

We report the first results of an experiment, in which explicit information on all velocity derivatives (the nine spatial derivatives, ∂ui∂xj, and the three temporal derivatives, ∂ui/∂t) along with the three components of velocity fluctuations at a Reynolds number as high asReλ~104is obtained. No use of the Taylor hypothesis was made, and this allowed us to obtain a variety of results concerning acceleration and its different Eulerian components along with vorticity, strain and other small-scale quantities. The field experiments were performed at five heights between 0.8 and 10m above the ground.The report consists of three parts. Part 1 is devoted to the description of facilities, methods and some general results. Part 2 concerns accelerations and related matters. Part 3 is devoted to the issues concerning temperature with the emphasis on joint statistics of temperature and velocity derivatives.

Kolmogorov’s contributions to the physical and geometrical understanding of small-scale turbulence and recent developments

1991 ◽  
Vol 434 (1890) ◽  
pp. 183-210 ◽  
Keyword(s):  
Turbulent Flows ◽  
Large Scale ◽  
Inertial Range ◽  
Small Scale ◽  
Small Scales ◽  
Recent Developments ◽  
Self Similar ◽  
Scale Turbulence ◽  
High Reynolds ◽  
Non Gaussian

This paper reviews how Kolmogorov postulated for the first time the existence of a steady statistical state for small-scale turbulence, and its defining parameters of dissipation rate and kinematic viscosity. Thence he made quantitative predictions of the statistics by extending previous methods of dimensional scaling to multiscale random processes. We present theoretical arguments and experimental evidence to indicate when the small-scale motions might tend to a universal form (paradoxically not necessarily in uniform flows when the large scales are gaussian and isotropic), and discuss the implications for the kinematics and dynamics of the fact that there must be singularities in the velocity field associated with the - 5/3 inertial range spectrum. These may be particular forms of eddy or ‘eigenstructure’ such as spiral vortices, which may not be unique to turbulent flows. Also, they tend to lead to the notable spiral contours of scalars in turbulence, whose self-similar structure enables the ‘box-counting’ technique to be used to measure the ‘capacity’ D K of the contours themselves or of their intersections with lines, D' K . Although the capacity, a term invented by Kolmogorov (and studied thoroughly by Kolmogorov & Tikhomirov), is like the exponent 2 p of a spectrum in being a measure of the distribution of length scales ( D' K being related to 2 p in the limit of very high Reynolds numbers), the capacity is also different in that experimentally it can be evaluated at local regions within a flow and at lower values of the Reynolds number. Thus Kolmogorov & Tikhomirov provide the basis for a more widely applicable measure of the self-similar structure of turbulence. Finally, we also review how Kolmogorov’s concept of the universal spatial structure of the small scales, together with appropriate additional physical hypotheses, enables other aspects of turbulence to be understood at these scales; in particular the general forms of the temporal statistics such as the high-frequency (inertial range) spectra in eulerian and lagrangian frames of reference, and the perturbations to the small scales caused by non-isotropic, non-gaussian and inhomogeneous large-scale motions.

Effect of Schmidt number on small-scale passive scalar turbulence

2003 ◽  
Vol 56 (6) ◽  
pp. 615-632 ◽  
Author(s):  
RA Antonia ◽  
P Orlandi
Keyword(s):  
Turbulent Flows ◽  
Schmidt Number ◽  
Isotropic Turbulence ◽  
Passive Scalar ◽  
Scalar Dissipation ◽  
Small Scale ◽  
Homogeneous Isotropic Turbulence ◽  
Passive Scalars ◽  
First Case ◽  
Decaying Turbulence

Previous reviews of the behavior of passive scalars which are convected and mixed by turbulent flows have focused primarily on the case when the Prandtl number Pr, or more generally, the Schmidt number Sc is around 1. The present review considers the extra effects which arise when Sc differs from 1. It focuses mainly on information obtained from direct numerical simulations of homogeneous isotropic turbulence which either decays or is maintained in steady state. The first case is of interest since it has attracted significant theoretical attention and can be related to decaying turbulence downstream of a grid. Topics covered in the review include spectra and structure functions of the scalar, the topology and isotropy of the small-scale scalar field, as well as the correlation between the fluctuating rate of strain and the scalar dissipation rate. In each case, the emphasis is on the dependence with respect to Sc. There are as yet unexplained differences between results on forced and unforced simulations of homogeneous isotropic turbulence. There are 144 references cited in this review article.

Extreme events and non-Kolmogorov spectra in turbulent flows behind two side-by-side square cylinders

2019 ◽  
Vol 874 ◽  
pp. 677-698 ◽  
Author(s):  
Yi Zhou ◽  
Koji Nagata ◽  
Yasuhiko Sakai ◽  
Tomoaki Watanabe
Keyword(s):  
Flow Regime ◽  
Turbulent Flows ◽  
Power Law ◽  
Extreme Events ◽  
Upstream Region ◽  
Velocity Fluctuations ◽  
Square Cylinders ◽  
Gap Flow ◽  
Power Law Exponent ◽  
Non Gaussian

Turbulent flows behind two side-by-side square cylinders with three different gap ratios, namely, $L_{d}/T_{0}=4,$ 6 and 8 ($L_{d}$ is the separation distance between two cylinders and $T_{0}$ is the cylinder thickness) are investigated by using direct numerical simulations. Depending on the strength of the gap flow, the three cases can generally be characterized into two regimes, one being the weak gap flow regime and the other being the robust gap flow regime. The wake-interaction length scale can only be applied to characterize the spatial evolution of the dual-wake flow in the robust gap flow regime. And only in this regime can the so-called ‘extreme events’ (i.e. non-Gaussian velocity fluctuations with large flatness) be identified. For the case with $L_{d}/T_{0}=6$, two downstream locations, i.e. $X/T_{0}=6$ and 26, at which the turbulent flows are highly non-Gaussian distributed and approximately Gaussian distributed, respectively, are analysed in detail. A well-defined $-5/3$ energy spectrum can be found in the near-field region (i.e. $X/T_{0}=6$), where the turbulent flow is still developing and highly intermittent and Kolmogorov’s universal equilibrium hypothesis does not hold. We confirm that the approximate $-5/3$ power law in the high-frequency range is closely related to the occurrences of the extreme events. As the downstream distance increases, the velocity fluctuations gradually adopt a Gaussian distribution, corresponding to a decrease in the strength of the extreme events. Consequently, the range of the $-5/3$ power law narrows. In the upstream region (i.e. $X/T_{0}=6$), the second-order structure function exhibits a power-law exponent close to $1$, whereas in the far downstream region (i.e. $X/T_{0}=26$) the expected $2/3$ power-law exponent appears. The larger exponent at $X/T_{0}=6$ is related to the fact that fluid motions in the intermediate range can directly ‘feel’ the large-scale vortex shedding.

Quantitative three-dimensional imaging and the structure of passive scalar fields in fully turbulent flows

1990 ◽  
Vol 216 ◽  
pp. 1-34 ◽  
Author(s):  
Rahul R. Prasad ◽  
K. R. Sreenivasan
Keyword(s):  
Turbulent Flows ◽  
Three Dimensional ◽  
Scalar Fields ◽  
Passive Scalar ◽  
Working Fluid ◽  
Small Scale ◽  
Main Body ◽  
Two Dimensional ◽  
Scaling Properties ◽  
Two Dimensional Images

The three-dimensional turbulent field of a passive scalar has been mapped quantitatively by obtaining, effectively instantaneously, several closely spaced parallel two-dimensional images; the two-dimensional images themselves have been obtained by laser-induced fluorescence. Turbulent jets and wakes at moderate Reynolds numbers are used as examples. The working fluid is water. The spatial resolution of the measurements is about four Kolmogorov scales. The first contribution of this work concerns the three-dimensional nature of the boundary of the scalar-marked regions (the ‘scalar interface’). It is concluded that interface regions detached from the main body are exceptional occurrences (if at all), and that in spite of the large structure, the randomness associated with small-scale convolutions of the interface are strong enough that any two intersections of it by parallel planes are essentially uncorrelated even if the separation distances are no more than a few Kolmogorov scales. The fractal dimension of the interface is determined directly by box-counting in three dimensions, and the value of 2.35 ± 0.04 is shown to be in good agreement with that previously inferred from two-dimensional sections. This justifies the use of the method of intersections. The second contribution involves the joint statistics of the scalar field and the quantity χ* (or its components), χ* being the appropriate approximation to the scalar ‘dissipation’ field in the inertial–convective range of scales. The third aspect relates to the multifractal scaling properties of the spatial intermittency of χ*; since all three components of χ* have been obtained effectively simultaneously, inferences concerning the scaling properties of the individual components and their sum have been possible. The usefulness of the multifractal approach for describing highly intermittent distributions of χ* and its components is explored by measuring the so-called singularity spectrum (or the f(α)-curve) which quantifies the spatial distribution of various strengths of χ*. Also obtained is a time sequence of two-dimensional images with the temporal resolution on the order of a few Batchelor timescales; this enables us to infer features of temporal intermittency in turbulent flows, and qualitatively the propagation speeds of the scalar interface. Finally, a few issues relating to the resolution effects have been addressed briefly by making point measurements with the spatial and temporal resolutions comparable with the Batchelor lengthscale and the corresponding timescale.

Is There an Asymptotic Effect of Initial and Upstream Conditions on Turbulence?

2008 ◽  
Author(s):  
William K. George
Keyword(s):  
Turbulent Flows ◽  
Turbulence Modeling ◽  
Initial Conditions ◽  
Single Point ◽  
Building Blocks ◽  
Asymptotic Independence ◽  
Point Model ◽  
Turbulence Control ◽  
The Past ◽  
Decaying Turbulence

More than two decades ago the first strong experimental results appeared suggesting that turbulent flows might not be asymptotically independent of their initial (or upstream) conditions [1]. And shortly thereafter the first theoretical explanations were offered as to why we came to believe something about turbulence that might not be true [2]. It was recognized immediately that if turbulence was indeed asymptotically independent of its initial conditions, it meant that there could be no universal single point model for turbulence [2], [3], certainly consistent with experience, but not easy to accept for the turbulence community. Even now the ideas of asymptotic independence still dominate most texts and teaching of turbulence. This paper reviews the substantial additional evidence — experimental, numerical and theoretical — for the asymptotic effect of initial and upstream conditions that has accumulated over the past 20 years. Emphasis has been placed on the canonical turbulent flows (especially wakes, jets, and homogeneous decaying turbulence), which have been the traditional building blocks for our understanding. Some of the implications for the future of turbulence modeling and research, especially LES and turbulence control, are also considered.

scholarly journals Rare transitions to thin-layer turbulent condensates

2019 ◽  
Vol 878 ◽  
pp. 356-369 ◽  
Author(s):  
Adrian van Kan ◽  
Takahiro Nemoto ◽  
Alexandros Alexakis
Keyword(s):  
Thin Layer ◽  
Turbulent Flows ◽  
Large Scale ◽  
Initial Conditions ◽  
Statistical Properties ◽  
Small Scale ◽  
Flow State ◽  
Stable States ◽  
Critical Height ◽  
Layer Height

Turbulent flows in a thin layer can develop an inverse energy cascade leading to spectral condensation of energy when the layer height is smaller than a certain threshold. These spectral condensates take the form of large-scale vortices in physical space. Recently, evidence for bistability was found in this system close to the critical height: depending on the initial conditions, the flow is either in a condensate state with most of the energy in the two-dimensional (2-D) large-scale modes, or in a three-dimensional (3-D) flow state with most of the energy in the small-scale modes. This bistable regime is characterised by the statistical properties of random and rare transitions between these two locally stable states. Here, we examine these statistical properties in thin-layer turbulent flows, where the energy is injected by either stochastic or deterministic forcing. To this end, by using a large number of direct numerical simulations (DNS), we measure the decay time $\unicode[STIX]{x1D70F}_{d}$ of the 2-D condensate to 3-D flow state and the build-up time $\unicode[STIX]{x1D70F}_{b}$ of the 2-D condensate. We show that both of these times $\unicode[STIX]{x1D70F}_{d},\unicode[STIX]{x1D70F}_{b}$ follow an exponential distribution with mean values increasing faster than exponentially as the layer height approaches the threshold. We further show that the dynamics of large-scale kinetic energy may be modelled by a stochastic Langevin equation. From time-series analysis of DNS data, we determine the effective potential that shows two minima corresponding to the 2-D and 3-D states when the layer height is close to the threshold.

Joint statistics of a passive scalar and its dissipation in turbulent flows

1994 ◽  
Vol 280 ◽  
pp. 173-197 ◽  
Author(s):  
F. Anselmet ◽  
H. Djeridi ◽  
L. Fulachier
Keyword(s):  
Correlation Coefficient ◽  
Turbulent Flows ◽  
Passive Scalar ◽  
Small Scale ◽  
Integral Scale ◽  
Low Frequencies ◽  
Skewness Factor ◽  
Combustion Modelling ◽  
The Asymmetry ◽  
Scale Properties

The statistical relationship between a passive scalar and its dissipation is important for both a basic understanding of turbulence small-scale properties and for various aspects of turbulent combustion modelling. This problem is studied in two different flows through spectral analysis as well as probability density functions using temperature as a passive scalar. Particular attention is paid to the experimental determination of the three squared derivatives involved in the temperature dissipation. As a first step, it is found that basic properties such as the correlation coefficient between temperature and its dissipation are strongly related to the asymmetry of the scalar fluctuations, so that the usually assumed statistical independence between these variables is not justified. These trends are the same for the two flows investigated here, a boundary layer and a jet. This connection appears to be related to fluctuations of small amplitude for both quantities which are associated with relatively low frequencies lying between the integral scale and the Taylor microscale. In regions where the temperature skewness factor is nearly zero, the correlation coefficient is also very small, and several tests show that the assumption of independence is then fully justified. Thus, the main parameter influencing joint statistics of temperature and its dissipation is the asymmetric feature of temperature fluctuations, but the asymmetry of the longitudinal temperature derivative, which results from the flow boundary conditions and is usually felt through the presence of the so-called temperature ramps, is also involved. Even though the magnitude of the derivative skewness factor is almost uniformly distributed in both flows, the secondary effect becomes the dominant one in flow regions where the influence of the temperature asymmetry is relatively weak.

Non-gaussian statistics of a passive scalar in turbulent flows

1998 ◽  
Vol 27 (1) ◽  
pp. 989-995 ◽  
Author(s):  
J. Mi ◽  
R.A. Antonia ◽  
G.J. Nathan ◽  
R.E. Luxton
Keyword(s):  
Turbulent Flows ◽  
Passive Scalar ◽  
Gaussian Statistics ◽  
Non Gaussian
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