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.

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.

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.

Characterization of Geometrical and Temporal Properties of Large-scale Motions in Turbulent Flows

2021 ◽  
Author(s):  
Christina Tsai ◽  
Kuang-Ting Wu
Keyword(s):  
Turbulent Flow ◽  
Turbulent Flows ◽  
Coherent Structures ◽  
Large Scale ◽  
Streamwise Velocity ◽  
Turbulent Structures ◽  
Temporal Properties ◽  
Turbulent Statistics ◽  
Spatial Locations

<p>It is demonstrated that turbulent boundary layers are populated by a hierarchy of recurrent structures, normally referred to as the coherent structures. Thus, it is desirable to gain a better understanding of the spatial-temporal characteristics of coherent structures and their impact on fluid particles. Furthermore, the ejection and sweep events play an important role in turbulent statistics. Therefore, this study focuses on the characterizations of flow particles under the influence of the above-mentioned two structures.</p><div><span>With regard to the geometry of turbulent structures, </span><span>Meinhart & Adrian (1995) </span>first highlighted the existence of large and irregularly shaped regions of uniform streamwise momentum zone (hereafter referred to as a uniform momentum zone, or UMZs), regions of relatively similar streamwise velocity with coherence in the streamwise and wall-normal directions.  <span>Subsequently, </span><span>de Silva et al. (2017) </span><span>provided a detection criterion that had previously been utilized to locate the uniform momentum zones (UMZ) and demonstrated the application of this criterion to estimate the spatial locations of the edges that demarcates UMZs.</span></div><div> </div><div>In this study, detection of the existence of UMZs is a pre-process of identifying the coherent structures. After the edges of UMZs are determined, the identification procedure of ejection and sweep events from turbulent flow DNS data should be defined. As such, an integrated criterion of distinguishing ejection and sweep events is proposed. Based on the integrated criterion, the statistical characterizations of coherent structures from available turbulent flow data such as event durations, event maximum heights, and wall-normal and streamwise lengths can be presented.</div>

scholarly journals On the structure of the self-sustaining cycle in separating and reattaching flows

2018 ◽  
Vol 857 ◽  
pp. 907-936 ◽  
Author(s):  
A. Cimarelli ◽  
A. Leonforte ◽  
D. Angeli
Keyword(s):  
Shear Layer ◽  
Rectangular Plate ◽  
Large Scale ◽  
Reverse Flow ◽  
Leading Edge ◽  
Streamwise Velocity ◽  
The Self ◽  
Small Scale ◽  
Spectral Evolution ◽  
Mean Velocity

The separating and reattaching flows and the wake of a finite rectangular plate are studied by means of direct numerical simulation data. The large amount of information provided by the numerical approach is exploited here to address the multi-scale features of the flow and to assess the self-sustaining mechanisms that form the basis of the main unsteadinesses of the flows. We first analyse the statistically dominant flow structures by means of three-dimensional spatial correlation functions. The developed flow is found to be statistically dominated by quasi-streamwise vortices and streamwise velocity streaks as a result of flow motions induced by hairpin-like structures. On the other hand, the reverse flow within the separated region is found to be characterized by spanwise vortices. We then study the spectral properties of the flow. Given the strongly inhomogeneous nature of the flow, the spectral analysis has been conducted along two selected streamtraces of the mean velocity field. This approach allows us to study the spectral evolution of the flow along its paths. Two well-separated characteristic scales are identified in the near-wall reverse flow and in the leading-edge shear layer. The first is recognized to represent trains of small-scale structures triggering the leading-edge shear layer, whereas the second is found to be related to a very large-scale phenomenon that embraces the entire flow field. A picture of the self-sustaining mechanisms of the flow is then derived. It is shown that very-large-scale fluctuations of the pressure field alternate between promoting and suppressing the reverse flow within the separation region. Driven by these large-scale dynamics, packages of small-scale motions trigger the leading-edge shear layers, which in turn created them, alternating in the top and bottom sides of the rectangular plate with a relatively long period of inversion, thus closing the self-sustaining cycle.

scholarly journals Finite Symmetries in Agent-Based Epidemic Models

2019 ◽  
Vol 24 (2) ◽  
pp. 44 ◽  
Author(s):  
Gilberto M. Nakamura ◽  
Ana Carolina P. Monteiro ◽  
George C. Cardoso ◽  
Alexandre S. Martinez
Keyword(s):  
Population Size ◽  
Transition Matrix ◽  
Large Scale ◽  
Initial Conditions ◽  
Disease Outbreaks ◽  
Epidemic Models ◽  
Small Scale ◽  
Stochastic Effects ◽  
Agent Based ◽  
Computational Performance

Predictive analysis of epidemics often depends on the initial conditions of the outbreak, the structure of the afflicted population, and population size. However, disease outbreaks are subjected to fluctuations that may shape the spreading process. Agent-based epidemic models mitigate the issue by using a transition matrix which replicates stochastic effects observed in real epidemics. They have met considerable numerical success to simulate small scale epidemics. The problem grows exponentially with population size, reducing the usability of agent-based models for large scale epidemics. Here, we present an algorithm that explores permutation symmetries to enhance the computational performance of agent-based epidemic models. Our findings bound the stochastic process to a single eigenvalue sector, scaling down the dimension of the transition matrix to o ( N 2 ) .

scholarly journals Post-rendezvous radar properties of comet 67P/CG from the Rosetta Mission: understanding future Earth-based radar observations and the dynamical evolution of comets

2019 ◽  
Vol 489 (2) ◽  
pp. 1667-1683 ◽  
Author(s):  
Essam Heggy ◽  
Elizabeth M Palmer ◽  
Alain Hérique ◽  
Wlodek Kofman ◽  
M Ramy El-Maarry
Keyword(s):  
Large Scale ◽  
Structural Changes ◽  
Dynamical Evolution ◽  
Textural Properties ◽  
Building Blocks ◽  
Cometary Nucleus ◽  
Small Scale ◽  
Small Bodies ◽  
Radar Observations ◽  
Comet 67P

ABSTRACT Radar observations provide crucial insights into the formation and dynamical evolution of comets. This ability is constrained by our knowledge of the dielectric and textural properties of these small-bodies. Using several observations by Rosetta as well as results from the Earth-based Arecibo radio telescope, we provide an updated and comprehensive dielectric and roughness description of Comet 67P/CG, which can provide new constraints on the radar properties of other nuclei. Furthermore, contrary to previous assumptions of cometary surfaces being dielectrically homogeneous and smooth, we find that cometary surfaces are dielectrically heterogeneous ( εr′≈1.6–3.2), and are rough at X- and S-band frequencies, which are widely used in characterization of small-bodies. We also investigate the lack of signal broadening in CONSERT observations through the comet head. Our results suggest that primordial building blocks in the subsurface are either absent, smaller than the radar wavelength, or have a weak dielectric contrast (Δ εr′). To constrain this ambiguity, we use optical albedo measurements by the OSIRIS camera of the freshly exposed subsurface after the Aswan cliff collapse. We find that the hypothetical subsurface blocks should have |Δ εr′|≳0.15, setting an upper limit of ∼ 1 m on the size of 67P/CG's primordial building blocks if they exist. Our analysis is consistent with a purely thermal origin for the ∼ 3 m surface bumps on pit walls and cliff-faces, hypothesized to be high-centred polygons formed from fracturing of the sintered shallow ice-bearing subsurface due to seasonal thermal expansion and contraction. Potential changes in 67P/CG's radar reflectivity at these at X- and S-bands can be associated with large-scale structural changes of the nucleus rather than small-scale textural ones. Monitoring changes in 67P/CG's radar properties during repeated close-approaches via Earth-based observations can constrain the dynamical evolution of its cometary nucleus.

Mixing layer produced by a screen and its dependence on initial conditions

1984 ◽  
Vol 142 ◽  
pp. 217-231 ◽  
Author(s):  
Hakuro Oguchi ◽  
Osamu Inoue
Keyword(s):  
Large Scale ◽  
Initial Conditions ◽  
Mixing Layer ◽  
Mixing Layers ◽  
Laser Doppler Velocimeter ◽  
Small Scale ◽  
Wire Screen ◽  
Flow Features ◽  
Wire Method ◽  
Layer Flow

This paper aims to elucidate the structure of the turbulent mixing layers, especially, its dependence on initial disturbances. The mixing layers are produced by setting a woven-wire screen perpendicular to the freestream in the test section of a wind tunnel to obstruct part of the flow. Three kinds of model geometry are treated; these model screens produced mixing layers which may be regarded as the equivalents of the plane mixing layer and of two-dimensional and axisymmetric wakes issuing into ambient streams of higher velocity. The initial disturbances are imposed by installing thin rods of various sizes along the edge of the screen or at the origin of the mixing layer. Flow features are visualized by the smoke-wire method. Statistical quantities are measured by a laser-Doppler velocimeter. In all cases large-scale transverse vortices seem to persist, although comparatively small-scale vortices are superimposed on the flow field in the mixing layer. The mixing layers are in self-preserving state at least up to third-order moments, but the self-preserving state is different in each case. The growth rates of the mixing layer are shown to depend strongly on the initial disturbance imposed.

On the survival of strong vortex filaments in ‘model’ turbulence

1999 ◽  
Vol 394 ◽  
pp. 261-279 ◽  
Author(s):  
ROBERTO VERZICCO ◽  
JAVIER JIMÉNEZ
Keyword(s):  
Turbulent Flows ◽  
Large Scale ◽  
Spatial Scales ◽  
Axial Strain ◽  
Compact Object ◽  
Mean Value ◽  
Theoretical Explanation ◽  
Small Scale ◽  
Vortex Filaments ◽  
Single Scale

This paper discusses numerical experiments in which an initially uniform columnar vortex is subject to several types of axisymmetric forcing that mimic the strain field of a turbulent flow. The mean value of the strain along the vortex axis is in all cases zero, and the vortex is alternately stretched and compressed. The emphasis is on identifying the parameter range in which the vortex survives indefinitely. This extends previous work in which the effect of steady single-scale non-uniform strains was studied. In a first series of experiments the effect of the unsteadiness of the forcing is analysed, and it is found that the vortex survives as a compact object if the ratio between the oscillation frequency and the strain itself is low enough. A theoretical explanation is given which agrees with the numerical results. The strain is then generalized to include several spatial scales and oscillation frequencies, with characteristics similar to those in turbulent flows. The largest velocities are carried by the large scales, while the highest gradients and faster time scales are associated with the shorter wavelengths. Also in these cases ‘infinitely long’ vortices are obtained which are more or less uniform and compact. Vorticity profiles averaged along their axes are approximately Gaussian. The radii obtained from these profiles are proportional to the Burgers' radius of the r.m.s. (small-scale) axial strain, while the azimuthal velocities are proportional to the maximum (large-scale) axial velocity differences. The study is motivated by previous observations of intense vortex filaments in turbulent flows, and the scalings found in the present experiments are consistent with those found in the turbulent simulations.

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.

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