scholarly journals Scaling of Low-Order Structure Functions in Homogeneous Turbulence

1996 ◽  
Vol 77 (18) ◽  
pp. 3799-3802 ◽  
Author(s):  
Nianzheng Cao ◽  
Shiyi Chen ◽  
Katepalli R. Sreenivasan
Keyword(s):  
Structure Functions ◽  
Homogeneous Turbulence ◽  
Order Structure ◽  
Low Order

LES computations and comparison with Kolmogorov theory for two-point pressure–velocity correlations and structure functions for globally anisotropic turbulence

2000 ◽  
Vol 403 ◽  
pp. 23-36 ◽  
Author(s):  
K. ALVELIUS ◽  
A. V. JOHANSSON
Keyword(s):  
Structure Functions ◽  
Homogeneous Turbulence ◽  
Kolmogorov Equation ◽  
Inertial Subrange ◽  
Order Structure ◽  
Velocity Correlation ◽  
Point Pressure ◽  
Decaying Turbulence ◽  
High Reynolds ◽  
Kolmogorov Theory

A new extension of the Kolmogorov theory, for the two-point pressure–velocity correlation, is studied by LES of homogeneous turbulence with a large inertial subrange in order to capture the high Reynolds number nonlinear dynamics of the flow. Simulations of both decaying and forced anisotropic homogeneous turbulence were performed. The forcing allows the study of higher Reynolds numbers for the same number of modes compared with simulations of decaying turbulence. The forced simulations give statistically stationary turbulence, with a substantial inertial subrange, well suited to test the Kolmogorov theory for turbulence that is locally isotropic but has significant anisotropy of the total energy distribution. This has been investigated in the recent theoretical studies of Lindborg (1996) and Hill (1997) where the role of the pressure terms was given particular attention. On the surface the two somewhat different approaches taken in these two studies may seem to lead to contradictory conclusions, but are here reconciled and (numerically) shown to yield an interesting extension of the traditional Kolmogorov theory. The results from the simulations indeed show that the two-point pressure–velocity correlation closely adheres to the predicted linear relation in the inertial subrange where also the pressure-related term in the general Kolmogorov equation is shown to vanish. Also, second- and third-order structure functions are shown to exhibit the expected dependences on separation.

Applicability of Kolmogorov's and Monin's equations of turbulence

1997 ◽  
Vol 353 ◽  
pp. 67-81 ◽  
Author(s):  
REGINALD J. HILL
Keyword(s):  
Structure Function ◽  
Structure Functions ◽  
Inertial Range ◽  
Homogeneous Turbulence ◽  
Order Structure ◽  
Third Order ◽  
Local Isotropy ◽  
The Third ◽  
Moderate Reynolds Number ◽  
Wide Range

The equation relating second- and third-order velocity structure functions was presented by Kolmogorov; Monin attempted to derive that equation on the basis of local isotropy. Recently, concerns have been raised to the effect that Kolmogorov's equation and an ancillary incompressibility condition governing the third-order structure function were proven only on the restrictive basis of isotropy and that the statistic involving pressure that appears in the derivation of Kolmogorov's equation might not vanish on the basis of local isotropy. These concerns are resolved. In so doing, results are obtained for the second- and third-order statistics on the basis of local homogeneity without use of local isotropy. These results are applicable to future studies of the approach toward local isotropy. Accuracy of Kolmogorov's equation is shown to be more sensitive to anisotropy of the third-order structure function than to anisotropy of the second-order structure function. Kolmogorov's 4/5 law for the inertial range of the third-order structure function is obtained without use of the incompressibility conditions on the second- and third-order structure functions. A generalization of Kolmogorov's 4/5 law, which applies to the inertial range of locally homogeneous turbulence at very large Reynolds numbers, is shown to also apply to the energy-containing range for the more restrictive case of stationary, homogeneous turbulence. The variety of derivations of Kolmogorov's and Monin's equations leads to a wide range of applicability to experimental conditions, including, in some cases, turbulence of moderate Reynolds number.

scholarly journals Anomalous scaling of low-order structure functions of turbulent velocity

2005 ◽  
Vol 533 ◽  
Author(s):  
S. Y. CHEN ◽  
B. DHRUVA ◽  
S. KURIEN ◽  
K. R. SREENIVASAN ◽  
M. A. TAYLOR
Keyword(s):  
Structure Functions ◽  
Turbulent Velocity ◽  
Order Structure ◽  
Anomalous Scaling ◽  
Low Order

A universal scaling for low-order structure functions in the log-law region of smooth- and rough-wall boundary layers

2014 ◽  
Vol 752 ◽  
pp. 140-156 ◽  
Author(s):  
P. A. Davidson ◽  
P.-Å. Krogstad
Keyword(s):  
Boundary Layers ◽  
Dissipation Rate ◽  
Structure Functions ◽  
Scaling Theory ◽  
Rough Wall ◽  
Large Reynolds Number ◽  
Order Structure ◽  
Wall Boundary ◽  
Log Law ◽  
Low Order

AbstractWe consider the log-law layer of both smooth- and rough-wall boundary layers at large Reynolds number. A scaling theory is proposed for low-order structure functions (say$\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}n \leq 6$) in the range of scales$\eta \ll r \ll \delta $, where$\eta $is the Kolmogorov length and$\delta $is the boundary layer thickness. This theory rests on the hypothesis that the turbulence in this intermediate range of scales depends only on the scale$r$, the local dissipation rate and the shear velocity. Crucially, the structure of the turbulence is assumed to be independent of the distance from the wall,$y$, except to the extent that$y$sets the value of the local dissipation rate. A detailed comparison is made between the predictions of the theory and data taken from both smooth- and rough-wall boundary layers. The data support the hypothesis that it is the dissipation rate, and not$y$, that controls the structure of the turbulence for this range of eddy sizes. Our findings provide the first unified scaling theory for both smooth- and rough-wall turbulence.

scholarly journals Characterizing sand ripples at equilibrium phases

2013 ◽  
Vol 61 (4) ◽  
pp. 293-298 ◽  
Author(s):  
Jie Qin ◽  
Deyu Zhong ◽  
Guangqian Wang
Keyword(s):  
Time Series ◽  
Random Fields ◽  
Morphological Characteristics ◽  
Structure Functions ◽  
Second Order ◽  
Order Structure ◽  
Two Dimensional ◽  
Sand Ripples ◽  
Digital Elevation ◽  
Equilibrium Phases

Abstract Morphological characteristics of ripples are analyzed considering bed surfaces as two dimensional random fields of bed elevations. Two equilibrium phases are analyzed with respect to successive development of ripples based on digital elevation models. The key findings relate to the shape of the two dimensional second-order structure functions and multiscaling behavior revealed by higher-order structure functions. Our results suggest that (1) the two dimensional second-order structure functions can be used to differentiate the two equilibrium phases of ripples; and (2) in contrast to the elevational time series of ripples that exhibit significant multiscaling behavior, the DEMs of ripples at both equilibrium phases do not exhibit multiscaling behavior.

Exact third-order structure functions for two-dimensional turbulence

2018 ◽  
Vol 851 ◽  
pp. 672-686 ◽  
Author(s):  
Jin-Han Xie ◽  
Oliver Bühler
Keyword(s):  
Structure Functions ◽  
Spectral Energy ◽  
Order Structure ◽  
Two Dimensional ◽  
Third Order ◽  
Transfer Rates ◽  
The Third ◽  
Random Forcing ◽  
Asymptotic Expressions ◽  
Special Case

We derive and investigate exact expressions for third-order structure functions in stationary isotropic two-dimensional turbulence, assuming a statistical balance between random forcing and dissipation both at small and large scales. Our results extend previously derived asymptotic expressions in the enstrophy and energy inertial ranges by providing uniformly valid expressions that apply across the entire non-dissipative range, which, importantly, includes the forcing scales. In the special case of white noise in time forcing this leads to explicit predictions for the third-order structure functions, which are successfully tested against previously published high-resolution numerical simulations. We also consider spectral energy transfer rates and suggest and test a simple robust diagnostic formula that is useful when forcing is applied at more than one scale.

scholarly journals Structure function measurements of the intermittent MHD turbulent cascade

1997 ◽  
Vol 4 (3) ◽  
pp. 185-199 ◽  
Author(s):  
T. S. Horbury ◽  
A. Balogh
Keyword(s):  
Energy Transfer ◽  
High Speed ◽  
Solar Wind Plasma ◽  
Turbulent Energy ◽  
Structure Functions ◽  
Order Structure ◽  
Data Sets ◽  
Magnetic Field Data ◽  
Spacecraft Data ◽  
Turbulent Cascade

Abstract. The intertmittent nature of turbulence within solar wind plasma has been demonstrated by several studies of spacecraft data. Using magnetic field data taken in high speed flows at high heliographic latitudes by the Ulysses probe, the character of fluctuations within the inertia] range is discussed. Structure functions are used extensively. A simple consideration of errors associated with calculations of high moment structure functions is shown to be useful as a practical estimate of the reliability of such calculations. For data sets of around 300 000 points, structure functions of moments above 5 are rarely reliable on the basis of this test, highlighting the importance of considering uncertainties in such calculations. When unreliable results are excluded, it is shown that inertial range polar fluctuations are well described by a multifractal model of turbulent energy transfer. Detailed consideration of the scaling of high order structure functions suggests energy transfer consistent with a "Kolmogorov" cascade.

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