scholarly journals Beyond Kolmogorov cascades

2019 ◽  
Vol 867 ◽  
Author(s):  
Bérengère Dubrulle
Keyword(s):  
Turbulent Flows ◽  
Large Scale ◽  
Scale Space ◽  
Energy Cascade ◽  
Cloud Formation ◽  
Small Scale ◽  
Weak Formulation ◽  
Anisotropic Flow ◽  
Energy Cascades ◽  
Homogeneity Hypothesis

The large-scale structure of many turbulent flows encountered in practical situations such as aeronautics, industry, meteorology is nowadays successfully computed using the Kolmogorov–Kármán–Howarth energy cascade picture. This theory appears increasingly inaccurate when going down the energy cascade that terminates through intermittent spots of energy dissipation, at variance with the assumed homogeneity. This is problematic for the modelling of all processes that depend on small scales of turbulence, such as combustion instabilities or droplet atomization in industrial burners or cloud formation. This paper explores a paradigm shift where the homogeneity hypothesis is replaced by the assumption that turbulence contains singularities, as suggested by Onsager. This paradigm leads to a weak formulation of the Kolmogorov–Kármán–Howarth–Monin equation (WKHE) that allows taking into account explicitly the presence of singularities and their impact on the energy transfer and dissipation. It provides a local in scale, space and time description of energy transfers and dissipation, valid for any inhomogeneous, anisotropic flow, under any type of boundary conditions. The goal of this article is to discuss WKHE as a tool to get a new description of energy cascades and dissipation that goes beyond Kolmogorov and allows the description of small-scale intermittency. It puts the problem of intermittency and dissipation in turbulence into a modern framework, compatible with recent mathematical advances on the proof of Onsager’s conjecture.

scholarly journals Span effect on the turbulence nature of flow past a circular cylinder

2019 ◽  
Vol 878 ◽  
pp. 306-323 ◽  
Author(s):  
Bernat Font Garcia ◽  
Gabriel D. Weymouth ◽  
Vinh-Tan Nguyen ◽  
Owen R. Tutty
Keyword(s):  
Circular Cylinder ◽  
Turbulent Flows ◽  
Large Scale ◽  
Three Dimensional ◽  
Small Scale ◽  
Flow Past ◽  
Energy Cascades ◽  
Flow Evolution ◽  
Scale Structures ◽  
Small Scale Structures

Turbulent flow evolution and energy cascades are significantly different in two-dimensional (2-D) and three-dimensional (3-D) flows. Studies have investigated these differences in obstacle-free turbulent flows, but solid boundaries have an important impact on the cross-over from 3-D to 2-D turbulence dynamics. In this work, we investigate the span effect on the turbulence nature of flow past a circular cylinder at $Re=10\,000$. It is found that even for highly anisotropic geometries, 3-D small-scale structures detach from the walls. Additionally, the natural large-scale rotation of the Kármán vortices rapidly two-dimensionalise those structures if the span is 50 % of the diameter or less. We show this is linked to the span being shorter than the Mode B instability wavelength. The conflicting 3-D small-scale structures and 2-D Kármán vortices result in 2-D and 3-D turbulence dynamics which can coexist at certain locations of the wake depending on the domain geometric anisotropy.

scholarly journals Inverse Energy Cascade in Advanced MHD Turbulence (the RNG Method)

1993 ◽  
Vol 157 ◽  
pp. 255-261
Author(s):  
N. Kleeorin ◽  
I. Rogachevskii
Keyword(s):  
Magnetic Field ◽  
Large Scale ◽  
Magnetic Field Effect ◽  
Magnetic Reynolds Number ◽  
Energy Cascade ◽  
Small Scale ◽  
Magnetic Fluctuations ◽  
Mhd Turbulence ◽  
Inverse Energy Cascade ◽  
Large Scale Magnetic Field

The nonlinear (in terms of the large-scale magnetic field) effect of the modification of the magnetic force by an advanced small-scale magnetohydrodynamic (MHD) turbulence is considered. The phenomenon is due to the generation of magnetic fluctuations at the expense of hydrodynamic pulsations. It results in a decrease of the elasticity of the large-scale magnetic field.The renormalization group (RNG) method was employed for the investigation of the MHD turbulence at the large magnetic Reynolds number. It was found that the level of the magnetic fluctuations can exceed that obtained from the equipartition assumption due to the inverse energy cascade in advanced MHD turbulence.This effect can excite an instability of the large-scale magnetic field due to the energy transfer from the small-scale turbulent pulsations. This instability is an example of the inverse energy cascade in advanced MHD turbulence. It may act as a mechanism for the large-scale magnetic ropes formation in the solar convective zone and spiral galaxies.

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.

Subgrid combustion modelling for large-eddy simulations

2000 ◽  
Vol 1 (2) ◽  
pp. 209-227 ◽  
Author(s):  
S Menon
Keyword(s):  
Turbulent Flows ◽  
Internal Combustion Engines ◽  
Large Scale ◽  
Large Eddy Simulations ◽  
Accurate Prediction ◽  
Pollutant Emissions ◽  
Combustion Model ◽  
Small Scale ◽  
Large Eddy ◽  
Combustion Processes

Next-generation gas turbine and internal combustion engines are required to reduce pollutant emissions significantly and also to be fuel efficient. Accurate prediction of pollutant formation requires proper resolution of the spatio-temporal evolution of the unsteady mixing and combustion processes. Since conventional steady state methods are not able to deal with these features, methodology based on large-eddy simulations (LESs) is becoming a viable choice to study unsteady reacting flows. This paper describes a new LES methodology developed recently that has demonstrated a capability to simulate reacting turbulent flows accurately. A key feature of this new approach is the manner in which small-scale turbulent mixing and combustion processes are simulated. This feature allows proper characterization of the effects of both large-scale convection and small-scale mixing on the scalar processes, thereby providing a more accurate prediction of chemical reaction effects. LESs of high Reynolds number premixed flames in the flamelet regime and in the distributed reaction regime are used to describe the ability of the new subgrid combustion model.

scholarly journals A multifractal model for the momentum transfer process in wall-bounded flows

2017 ◽  
Vol 824 ◽  
Author(s):  
X. I. A. Yang ◽  
A. Lozano-Durán
Keyword(s):  
Turbulent Flows ◽  
Large Scale ◽  
Isotropic Turbulence ◽  
Small Scale ◽  
Length Scale ◽  
Cascade Process ◽  
Outer Length ◽  
Multifractal Formalism ◽  
Multiplicative Process ◽  
Stress Fluctuation

The cascading process of turbulent kinetic energy from large-scale fluid motions to small-scale and lesser-scale fluid motions in isotropic turbulence may be modelled as a hierarchical random multiplicative process according to the multifractal formalism. In this work, we show that the same formalism might also be used to model the cascading process of momentum in wall-bounded turbulent flows. However, instead of being a multiplicative process, the momentum cascade process is additive. The proposed multifractal model is used for describing the flow kinematics of the low-pass filtered streamwise wall-shear stress fluctuation $\unicode[STIX]{x1D70F}_{l}^{\prime }$, where $l$ is the filtering length scale. According to the multifractal formalism, $\langle {\unicode[STIX]{x1D70F}^{\prime }}^{2}\rangle \sim \log (Re_{\unicode[STIX]{x1D70F}})$ and $\langle \exp (p\unicode[STIX]{x1D70F}_{l}^{\prime })\rangle \sim (L/l)^{\unicode[STIX]{x1D701}_{p}}$ in the log-region, where $Re_{\unicode[STIX]{x1D70F}}$ is the friction Reynolds number, $p$ is a real number, $L$ is an outer length scale and $\unicode[STIX]{x1D701}_{p}$ is the anomalous exponent of the momentum cascade. These scalings are supported by the data from a direct numerical simulation of channel flow at $Re_{\unicode[STIX]{x1D70F}}=4200$.

scholarly journals Children with autism are neither systematic nor optimal foragers

2010 ◽  
Vol 108 (1) ◽  
pp. 421-426 ◽  
Author(s):  
Elizabeth Pellicano ◽  
Alastair D. Smith ◽  
Filipe Cristino ◽  
Bruce M. Hood ◽  
Josie Briscoe ◽  
...  
Keyword(s):  
Large Scale ◽  
Search Task ◽  
Good Reason ◽  
Search Behavior ◽  
Children With Autism ◽  
Scale Space ◽  
School Age Children ◽  
Small Scale ◽  
Search Patterns ◽  
Target Locations

It is well established that children with autism often show outstanding visual search skills. To date, however, no study has tested whether these skills, usually assessed on a table-top or computer, translate to more true-to-life settings. One prominent account of autism, Baron-Cohen's “systemizing” theory, gives us good reason to suspect that they should. In this study, we tested whether autistic children's exceptional skills at small-scale search extend to a large-scale environment and, in so doing, tested key claims of the systemizing account. Twenty school-age children with autism and 20 age- and ability-matched typical children took part in a large-scale search task in the “foraging room”: a purpose-built laboratory, with numerous possible search locations embedded into the floor. Children were instructed to search an array of 16 (green) locations to find the hidden (red) target as quickly as possible. The distribution of target locations was manipulated so that they appeared on one side of the midline for 80% of trials. Contrary to predictions of the systemizing account, autistic children's search behavior was much less efficient than that of typical children: they showed reduced sensitivity to the statistical properties of the search array, and furthermore, their search patterns were strikingly less optimal and less systematic. The nature of large-scale search behavior in autism cannot therefore be explained by a facility for systemizing. Rather, children with autism showed difficulties exploring and exploiting the large-scale space, which might instead be attributed to constraints (rather than benefits) in their cognitive repertoire.

Inefficient Search of Large-Scale Space in Williams Syndrome: Further Insights on the Role of LIMK1 Deletion in Deficits of Spatial Cognition

Perception ◽  
10.1068/p6050 ◽  
2009 ◽  
Vol 38 (5) ◽  
pp. 694-701 ◽  
Author(s):  
Alastair D Smith ◽  
Iain D Gilchrist ◽  
Bruce Hood ◽  
May Tassabehji ◽  
Annette Karmiloff-Smith
Keyword(s):  
Spatial Cognition ◽  
Williams Syndrome ◽  
Large Scale ◽  
Genetic Disorder ◽  
Search Space ◽  
Scale Space ◽  
Chromosome 7 ◽  
Small Scale ◽  
Lim Kinase ◽  
Lim Kinase 1

Williams syndrome (WS) is a genetic disorder associated with impairments of spatial cognition. This has primarily been studied in small-scale space, and rarely in large-scale environments. In order to fully characterise the spatial deficits in WS, and also to address claims that the deletion of LIM-kinase 1 (LIMK1) on chromosome 7 is responsible for those deficits, we report an automated large-scale search task for humans that places the participant egocentrically within the search space. Search locations were defined as lights and switches embedded in the floor, and participants attempted to locate a hidden target by pressing the switch at potential locations. We compared individuals with WS to patients with smaller deletions (including LIMK1) in the critical region on chromosome 7. Whilst partial-deletion participants performed efficiently on the task, participants with WS demonstrated inefficient search profiles: their search slopes were steeper and they made significantly more erroneous revisits to previously inspected locations. Our findings indicate that spatial deficits associated with WS also affect large-scale spatial processing and suggest that hemizygous deletion of LIMK1 is not sufficient to account for any of the spatial deficits associated with WS.

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 Statistical Analysis of Dynamic Subgrid Modeling Approaches in Large Eddy Simulation

2021 ◽  
Author(s):  
Mohammad Khalid Hossen ◽  
Asokan Mulayath Variyath ◽  
Jahrul M Alam
Keyword(s):  
Kinetic Energy ◽  
Large Eddy Simulation ◽  
Turbulent Flows ◽  
Large Scale ◽  
Physical Space ◽  
Statistical Characteristics ◽  
Small Scale ◽  
Eddy Simulation ◽  
Wide Range ◽  
Large Eddy

In large eddy simulation (LES) of turbulent flows, the most critical dynamical processes to be considered by dynamic subgrid models to account for an average cascade of kinetic energy from the largest to the smallest scales of the flow is not fully clear. Furthermore, evidence of vortex stretching being the primary mechanism of the cascade is not out of the question. In this article, we study some essential statistical characteristics of vortex stretching and its role in dynamic approaches of modeling subgrid-scale turbulence. We have compared the interaction of subgrid stresses with the filtered quantities among four models using invariants of the velocity gradient tensor. This technique is a single unified approach to studying a wide range of length scales in the turbulent flow. In addition, it also provides a rational basis for the statistical characteristics a subgrid model must serve in physical space to ensure an appropriate cascade of kinetic energy. Results indicate that the stretching mechanism extracts energy from the large-scale straining motion and passes it onto small-scale stretched vortices.

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