The integral scale in homogeneous isotropic turbulence

2002 ◽  
Vol 459 ◽  
pp. 429-443 ◽  
Author(s):  
HONGLU WANG ◽  
WILLIAM K. GEORGE
Keyword(s):  
Isotropic Turbulence ◽  
Power Laws ◽  
Spectral Model ◽  
Homogeneous Isotropic Turbulence ◽  
Integral Scale ◽  
Integral Scales ◽  
Order Of Magnitude ◽  
Decaying Turbulence ◽  
Statistical Sample ◽  
Almost All

A simple spectral model is used to examine what is required to determine the energy and integral scale in homogeneous isotropic turbulence. The problem is that these are determined in part by the largest scales of the turbulence which are either not simulated at all by DNS or experiments, or cannot be estimated because of an insufficient statistical sample. The absence of scales an order of magnitude below the peak in the energy spectrum is shown to affect the determination significantly. Since this energy peak shifts to lower wavenumbers as the flow evolves, the problem becomes progressively worse during decay. It is suggested that almost all reported integral scales for isotropic decaying turbulence are questionable, and that the power laws fitted to them are seriously in error. Approximate correction using the spectral model shows that recent DNS data which decay as u2 ∝ tn with constant n, are also consistent with L ∝ t1/2.

scholarly journals The non-equilibrium region of grid-generated decaying turbulence

2014 ◽  
Vol 744 ◽  
pp. 5-37 ◽  
Author(s):  
P. C. Valente ◽  
J. C. Vassilicos
Keyword(s):  
Turbulent Flows ◽  
Integral Scale ◽  
Dissipation Coefficient ◽  
Integral Scales ◽  
Usual Equilibrium ◽  
Decaying Turbulence ◽  
Equilibrium Region ◽  
Non Equilibrium

AbstractThe previously reported non-equilibrium dissipation law is investigated in turbulent flows generated by various regular and fractal square grids. The flows are documented in terms of various turbulent profiles which reveal their differences. In spite of significant inhomogeneity and anisotropy differences, the new non-equilibrium dissipation law is observed in all of these flows. Various transverse and longitudinal integral scales are measured and used to define the dissipation coefficient $C_{\varepsilon }$. It is found that the new non-equilibrium dissipation law is not an artefact of a particular choice of the integral scale and that the usual equilibrium dissipation law can actually coexist with the non-equilibrium law in different regions of the same flow.

scholarly journals Direct Numerical Simulation in Two Dimensional Homogeneous Isotropic Turbulence Using Spectral Method

2013 ◽  
Vol 5 (3) ◽  
pp. 435-445
Author(s):  
M. S. I. Mallik ◽  
M. A. Uddin ◽  
M. A. Rahman
Keyword(s):  
Numerical Simulation ◽  
Reynolds Number ◽  
Flow Field ◽  
Direct Numerical Simulation ◽  
Spectral Method ◽  
Isotropic Turbulence ◽  
Qualitative Behavior ◽  
Two Dimensional ◽  
Homogeneous Isotropic Turbulence ◽  
Decaying Turbulence

Direct numerical simulation (DNS) in two-dimensional homogeneous isotropic turbulence is performed by using the Spectral method at a Reynolds number Re = 1000 on a uniformly distributed grid points. The Reynolds number is low enough that the computational grid is capable of resolving all the possible turbulent scales. The statistical properties in the computed flow field show a good agreement with the qualitative behavior of decaying turbulence. The behavior of the flow structures in the computed flow field also follow the classical idea of the fluid flow in turbulence. Keywords: Direct numerical simulation, Isotropic turbulence, Spectral method. © 2013 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved. doi:http://dx.doi.org/10.3329/jsr.v5i3.12665 J. Sci. Res. 5 (3), 435-445 (2013)  

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.

scholarly journals Radar cross sections for mesospheric echoes at Jicamarca

2009 ◽  
Vol 27 (7) ◽  
pp. 2675-2684 ◽  
Author(s):  
G. A. Lehmacher ◽  
E. Kudeki ◽  
A. Akgiray ◽  
L. Guo ◽  
P. Reyes ◽  
...  
Keyword(s):  
Cross Sections ◽  
Isotropic Turbulence ◽  
Solar Proton ◽  
Thin Layers ◽  
Turbulence Theory ◽  
Homogeneous Isotropic Turbulence ◽  
Radar Cross Sections ◽  
Order Of Magnitude ◽  
Summer Echoes ◽  
Thick Layers

Abstract. Radar cross sections (RCS) of mesospheric layers at 50 MHz observed at Jicamarca, Peru, range from 10−18 to 10−16 m−1, three orders of magnitudes smaller than cross sections reported for polar mesospheric winter echoes during solar proton events and six orders of magnitude smaller than polar mesospheric summer echoes. Large RCS are found in thick layers around 70 km that also show wide radar spectra, which is interpreted as turbulent broadening. For typical atmospheric and ionospheric conditions, volume scattering RCS for stationary, homogeneous, isotropic turbulence at 3 m are also in the range 10−18 to 10−16 m−1, in reasonable agreement with measurements. Moreover, theory predicts maximum cross sections around 70 km, also in agreement with observations. Theoretical values are still a matter of order-of-magnitude estimation, since the Bragg scale of 3 m is near or inside the viscous subrange, where the form of the turbulence spectrum is not well known. In addition, steep electron density gradients can increase cross-sections significantly. For thin layers with large RCS and narrow spectra, isotropic turbulence theory fails and scattering or reflection from anisotropic irregularities may gain relevance.

scholarly journals Passive scalar decay laws in isotropic turbulence: Prandtl number effects

2015 ◽  
Vol 784 ◽  
pp. 274-303 ◽  
Author(s):  
A. Briard ◽  
T. Gomez ◽  
P. Sagaut ◽  
S. Memari
Keyword(s):  
Isotropic Turbulence ◽  
Power Laws ◽  
Passive Scalar ◽  
Initial Position ◽  
Scalar Dissipation ◽  
Integral Scale ◽  
Temporal Decay ◽  
Wide Range ◽  
Prandtl Numbers ◽  
High Reynolds

The passive scalar dynamics in a freely decaying turbulent flow is studied. The classical framework of homogeneous isotropic turbulence without forcing is considered. Both low and high Reynolds number regimes are investigated for very small and very large Prandtl numbers. The long time behaviours of integrated quantities such as the scalar variance or the scalar dissipation rate are analysed by considering that the decay follows power laws. This study addresses three major topics. First, the Comte-Bellot and Corrsin (CBC) dimensional analysis for the temporal decay exponents is extended to the case of a passive scalar when the permanence of large eddies is broken. Secondly, using numerical simulations based on an eddy-damped quasi-normal Markovian (EDQNM) model, the time evolution of integrated quantities is accurately determined for a wide range of Reynolds and Prandtl numbers. These simulations show that, whatever the values of the Reynolds and the Prandtl numbers are, the decay follows an algebraic law with an exponent very close to the value predicted by the CBC theory. Finally, the initial position of the scalar integral scale$L_{T}$has no influence on the asymptotic values of the decay exponents, and an analytical law predicting the relative positions of the kinetic and scalar spectra peaks is derived.

scholarly journals Universality in Decaying Turbulence at High Reynolds Numbers

2021 ◽  
Author(s):  
Christian Kuechler ◽  
Gergory Bewley ◽  
Eberhard Bodenschatz
Keyword(s):  
Isotropic Turbulence ◽  
Power Laws ◽  
Reynolds Numbers ◽  
Variable Density ◽  
Scaling Exponent ◽  
Max Planck ◽  
Self Similarity ◽  
Extended Self ◽  
Variable Density Turbulence ◽  
Decaying Turbulence

Abstract In the limit of very large Reynolds numbers for homogeneous isotropic turbulence of an incompressible fluid, the statistics of the velocity differences between two points in space are expected to approach universal power laws at scales smaller than those at which energy is injected. Even at the highest Reynolds numbers available in laboratory and natural flows such universal power laws have remained elusive. On the other hand, power laws have been observed empirically in derived quantities, namely in the relative scaling in statistics of different orders according to the Extended Self Similarity hypothesis. Here we present experimental results from the Max Planck Variable Density Turbulence Tunnel over an unprecedented range of Reynolds numbers. We find that the velocity difference statistics take a universal functional form that is distinct from a power law. By applying a self-similar model derived for decaying turbulence to our data, an effective scaling exponent for the second moment can be derived that agrees well with that obtained from Extended Self Similarity.

Kármán–Howarth solutions of homogeneous isotropic turbulence

2021 ◽  
Vol 932 ◽  
Author(s):  
L. Djenidi ◽  
R.A. Antonia
Keyword(s):  
Reynolds Number ◽  
Large Scale ◽  
Isotropic Turbulence ◽  
Three Dimensional ◽  
Order Moment ◽  
Homogeneous Isotropic Turbulence ◽  
The Difference ◽  
Decaying Turbulence ◽  
The Impact ◽  
Good Agreement

The Kármán–Howarth equation (KHEq) is solved using a closure model to obtain solutions of the second-order moment of the velocity increment, $S_2$ , in homogeneous isotropic turbulence (HIT). The results are in good agreement with experimental data for decaying turbulence and are also consistent with calculations based on the three-dimensional energy spectrum for decaying HIT. They differ, however, from those for forced HIT, the difference occurring mainly at large scales. This difference is attributed to the fact that the forcing generates large-scale motions which are not compatible with the KHEq. As the Reynolds number increases, the impact of forcing on the small scales decreases, thus allowing the KHEq and spectrally based solutions to agree well in the range of scales unaffected by forcing. Finally, the results show that the two-thirds law is compatible with the KHEq solutions as the Reynolds number increases to very large, if not infinite, values.

TRACKING OF VORTICAL STRUCTURES IN THREE-DIMENSIONAL DECAYING HOMOGENEOUS ISOTROPIC TURBULENCE

2011 ◽  
Vol 22 (12) ◽  
pp. 1373-1391 ◽  
Author(s):  
WALEED ABDEL-KAREEM
Keyword(s):  
Velocity Field ◽  
Flow Field ◽  
Isotropic Turbulence ◽  
Three Dimensional ◽  
Statistical Characteristics ◽  
Vortex Rings ◽  
Homogeneous Isotropic Turbulence ◽  
Vortical Structures ◽  
Decaying Turbulence ◽  
Boltzmann Method

Direct numerical simulation of three-dimensional decaying homogeneous isotropic turbulence with a resolution of 1283 is carried out using the Lattice Boltzmann Method (LBM). The aim of this paper is to investigate the statistical characteristics of the obtained turbulent flow field and the behavior of the vortical structures. Most of the LBM simulations of decaying turbulence were mainly focused on the statistical results of the velocity field, however the characteristics of the coherent vortices and their time evolution are ignored. In this paper, the statistical properties of the velocity field as well as the extraction and tracking processes of individual vortices are considered. Results show that the present simulation could recover important features of turbulence such as isotropy, skewness, energy spectrum and elongated vortical structures. A vortex ring is identified in the flow field which can be considered as a sign for the existence of vortex rings in homogeneous isotropic turbulence. Forward and reverse tracking of individual vortical structures shows that vortex rings can be generated from the interaction and the overlapping of vortex tubes.

Small-scale energy cascade in homogeneous isotropic turbulence

2019 ◽  
Vol 4 (10) ◽  
Author(s):  
Mohamad Ibrahim Cheikh ◽  
James Chen ◽  
Mingjun Wei
Keyword(s):  
Isotropic Turbulence ◽  
Energy Cascade ◽  
Small Scale ◽  
Homogeneous Isotropic Turbulence
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