Modeling the third-order velocity structure function in the scaling range at finite Reynolds numbers

2021 ◽  
Vol 62 (8) ◽  
pp. 083102
Author(s):  
L. Djenidi ◽  
R. A. Antonia
Keyword(s):  
Structure Function ◽  
Velocity Structure ◽  
Reynolds Numbers ◽  
Third Order ◽  
The Third ◽  
Velocity Structure Function

Approach to the 4/3 law for turbulent pipe and channel flows examined through a reformulated scale-by-scale energy budget

2021 ◽  
Vol 931 ◽  
Author(s):  
Spencer J. Zimmerman ◽  
R.A. Antonia ◽  
L. Djenidi ◽  
J. Philip ◽  
J.C. Klewicki
Keyword(s):  
Reynolds Number ◽  
Structure Function ◽  
Energy Budget ◽  
Velocity Structure ◽  
Third Order ◽  
The Third ◽  
Velocity Structure Function ◽  
Budget Equation ◽  
Rate Of Emergence ◽  
High Reynolds

In this study, we propose a scale-by-scale (SBS) energy budget equation for flows with homogeneity in at least one direction. This SBS budget represents a modified form of the equation first proposed by Danaila et al. (J. Fluid Mech., vol. 430, 2001, pp. 87–109) for the channel centreline – the primary difference is that, here, we consider the role of pressure along with the errors associated with the isotropic approximations of the interscale divergence and Laplacian of the squared velocity increment. The term encompassing the effects of mean shear is also characterised such that the present analysis can be extended straightforwardly to locations away from the centreline. We show, based on a detailed analysis of previously published channel flow direct numerical simulations and pipe flow experiments near the centreline, how several terms in the present SBS budget equation (including the third-order velocity structure function) behave with increasing Reynolds number. The behaviour of these terms is shown to imply a rate of emergence and subsequent growth of the 4/3 law scale subrange at the channel centreline and pipe axis. The analysis also suggests that the peak magnitude of the third-order velocity structure function occurs at a scale that is fixed in proportion to the Taylor microscale at sufficiently high Reynolds number.

Finite Reynolds number effect on the scaling range behaviour of turbulent longitudinal velocity structure functions

2017 ◽  
Vol 820 ◽  
pp. 341-369 ◽  
Author(s):  
S. L. Tang ◽  
R. A. Antonia ◽  
L. Djenidi ◽  
L. Danaila ◽  
Y. Zhou
Keyword(s):  
Reynolds Number ◽  
Structure Function ◽  
Large Scale ◽  
Velocity Structure ◽  
Longitudinal Velocity ◽  
Structure Functions ◽  
Third Order ◽  
Reynolds Number Effect ◽  
Rate Of Increase ◽  
Velocity Structure Function

The effect of large-scale forcing on the second- and third-order longitudinal velocity structure functions, evaluated at the Taylor microscale $r=\unicode[STIX]{x1D706}$, is assessed in various turbulent flows at small to moderate values of the Taylor microscale Reynolds number $R_{\unicode[STIX]{x1D706}}$. It is found that the contribution of the large-scale terms to the scale by scale energy budget differs from flow to flow. For a fixed $R_{\unicode[STIX]{x1D706}}$, this contribution is largest on the centreline of a fully developed channel flow but smallest for stationary forced periodic box turbulence. For decaying-type flows, the contribution lies between the previous two cases. Because of the difference in the large-scale term between flows, the third-order longitudinal velocity structure function at $r=\unicode[STIX]{x1D706}$ differs from flow to flow at small to moderate $R_{\unicode[STIX]{x1D706}}$. The effect on the second-order velocity structure functions appears to be negligible. More importantly, the effect of $R_{\unicode[STIX]{x1D706}}$ on the scaling range exponent of the longitudinal velocity structure function is assessed using measurements of the streamwise velocity fluctuation $u$, with $R_{\unicode[STIX]{x1D706}}$ in the range 500–1100, on the axis of a plane jet. It is found that the magnitude of the exponent increases as $R_{\unicode[STIX]{x1D706}}$ increases and the rate of increase depends on the order $n$. The trend of published structure function data on the axes of an axisymmetric jet and a two-dimensional wake confirms this dependence. For a fixed $R_{\unicode[STIX]{x1D706}}$, the exponent can vary from flow to flow and for a given flow, the larger $R_{\unicode[STIX]{x1D706}}$ is, the closer the exponent is to the value predicted by Kolmogorov (Dokl. Akad. Nauk SSSR, vol. 30, 1941a, pp. 299–303) (hereafter K41). The major conclusion is that the finite Reynolds number effect, which depends on the flow, needs to be properly accounted for before determining whether corrections to K41, arising from the intermittency of the energy dissipation rate, are needed. We further point out that it is imprudent, if not incorrect, to associate the finite Reynolds number effect with a consequence of the modified similarity hypothesis introduced by Kolmogorov (J. Fluid Mech., vol. 13, 1962, pp. 82–85) (K62); we contend that this association has misled the vast majority of post K62 investigations of the consequences of K62.

scholarly journals Third-order structure functions in rotating and stratified turbulence: a comparison between numerical, analytical and observational results

2014 ◽  
Vol 755 ◽  
pp. 294-313 ◽  
Author(s):  
Enrico Deusebio ◽  
P. Augier ◽  
E. Lindborg
Keyword(s):  
Structure Function ◽  
Velocity Structure ◽  
Structure Functions ◽  
Energy Cascade ◽  
Order Structure ◽  
Temperature Structure ◽  
Stratified Turbulence ◽  
Third Order ◽  
The Third ◽  
Spectral Flux

AbstractFirst, we review analytical and observational studies on third-order structure functions including velocity and buoyancy increments in rotating and stratified turbulence and discuss how these functions can be used in order to estimate the flux of energy through different scales in a turbulent cascade. In particular, we suggest that the negative third-order velocity–temperature–temperature structure function that was measured by Lindborg & Cho (Phys. Rev. Lett., vol. 85, 2000, p. 5663) using stratospheric aircraft data may be used in order to estimate the downscale flux of available potential energy (APE) through the mesoscales. Then, we calculate third-order structure functions from idealized simulations of forced stratified and rotating turbulence and compare with mesoscale results from the lower stratosphere. In the range of scales with a downscale energy cascade of kinetic energy (KE) and APE we find that the third-order structure functions display a negative linear dependence on separation distance $\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}} r $, in agreement with observation and supporting the interpretation of the stratospheric data as evidence of a downscale energy cascade. The spectral flux of APE can be estimated from the relevant third-order structure function. However, while the sign of the spectral flux of KE is correctly predicted by using the longitudinal third-order structure functions, its magnitude is overestimated by a factor of two. We also evaluate the third-order velocity structure functions that are not parity invariant and therefore display a cyclonic–anticyclonic asymmetry. In agreement with the results from the stratosphere, we find that these functions have an approximate $ r^{2} $-dependence, with strong dominance of cyclonic motions.

scholarly journals Intermittency, Moments, and Friction Coefficient during the Subcritical Transition of Channel Flow

Entropy ◽  
2020 ◽  
Vol 22 (12) ◽  
pp. 1399
Author(s):  
Jinsheng Liu ◽  
Yue Xiao ◽  
Mogeng Li ◽  
Jianjun Tao ◽  
Shengjin Xu
Keyword(s):  
Friction Coefficient ◽  
Turbulence Intensity ◽  
Reynolds Numbers ◽  
Test Case ◽  
Structure Model ◽  
Turbulent Structures ◽  
Third Order ◽  
Low Reynolds Numbers ◽  
The Third ◽  
High Turbulence

The intermittent distribution of localized turbulent structures is a key feature of the subcritical transitions in channel flows, which are studied in this paper with a wind channel and theoretical modeling. Entrance disturbances are introduced by small beads, and localized turbulent patches can be triggered at low Reynolds numbers (Re). High turbulence intensity represents strong ability of perturbation spread, and a maximum turbulence intensity is found for every test case as Re ≥ 950, where the turbulence fraction increases abruptly with Re. Skewness can reflect the velocity defects of localized turbulent patches and is revealed to become negative when Re is as low as about 660. It is shown that the third-order moments of the midplane streamwise velocities have minima, while the corresponding forth-order moments have maxima during the transition. These kinematic extremes and different variation scenarios of the friction coefficient during the transition are explained with an intermittent structure model, where the robust localized turbulent structure is simplified as a turbulence unit, a structure whose statistical properties are only weak functions of the Reynolds number.

MULTIFRACTAL CASCADE SYMMETRY MODEL FOR FULLY DEVELOPED TURBULENCE

Fractals ◽  
2018 ◽  
Vol 26 (04) ◽  
pp. 1850070
Author(s):  
G. C. LAYEK ◽  
SUNITA
Keyword(s):  
Structure Function ◽  
Symmetry Group ◽  
Velocity Structure ◽  
Random Parameter ◽  
Continuous Symmetry ◽  
Space Filling ◽  
Support Set ◽  
Developed Turbulence ◽  
Symmetry Model ◽  
Velocity Structure Function

We report a symmetry model for turbulence intermittency. This is obtained by the compositions of continuous symmetry group transformations of statistical turbulent spectral equation at infinite Reynolds number limit. Flow evolution under group compositions yields velocity structure function exponents that depend on the dilation symmetry group parameter [Formula: see text] [Formula: see text] and a random parameter [Formula: see text]. The random parameter [Formula: see text] is associated with energy distribution. Since the correction to the space-filling Kolmogorov cascade is small, the value of [Formula: see text]. The asymptotic structures are filaments having dimension one, so [Formula: see text] is found to be related with [Formula: see text] by [Formula: see text]. The present model therefore depends only on [Formula: see text], and [Formula: see text] can be ascertained uniquely for [Formula: see text]. It is found that the velocity structure function exponents [Formula: see text], [Formula: see text] in present symmetry model agree well with the existing experimental, direct numerical simulation results and different phenomenological models for [Formula: see text]. For these values of [Formula: see text], the correction to Kolmogorov space-filling, universal [Formula: see text] law, belongs to the range [Formula: see text], and the fractal dimension for the support set lies in [Formula: see text].

Doppler lidar alerting algorithm of low-level turbulence based on velocity structure function

2017 ◽  
Vol 46 (10) ◽  
pp. 1030005
Author(s):  
熊兴隆 Xiong Xinglong ◽  
韩永安 Han Yong′an ◽  
蒋立辉 Jiang Lihui ◽  
陈柏纬 Chen Bowei ◽  
陈 星 Chen Xing
Keyword(s):  
Structure Function ◽  
Velocity Structure ◽  
Doppler Lidar ◽  
Low Level ◽  
Velocity Structure Function

scholarly journals Structure function analysis and intermittency in the atmospheric boundary layer

2008 ◽  
Vol 15 (6) ◽  
pp. 915-929 ◽  
Author(s):  
J. M. Vindel ◽  
C. Yagüe ◽  
J. M. Redondo
Keyword(s):  
Structure Function ◽  
Velocity Structure ◽  
Function Analysis ◽  
Inertial Range ◽  
Order Structure ◽  
Turbulence Structure ◽  
Scaling Exponent ◽  
Local Similarity ◽  
Velocity Structure Function ◽  
Velocity Increments

Abstract. Data from the SABLES98 experimental campaign (Cuxart et al., 2000) have been used in order to study the relationship of the probability distribution of velocity increments (PDFs) to the scale and the degree of stability. This connection is demonstrated by means of the velocity structure functions and the PDFs of the velocity increments. Using the hypothesis of local similarity, so that the third order structure function scaling exponent is one, the inertial range in the Kolmogorov sense has been identified for different conditions, obtaining the velocity structure function scaling exponents for several orders. The degree of intermittency in the energy cascade is measured through these exponents and compared with the forcing intermittency revealed through the evolution of flatness with scale. The role of non-homogeneity in the turbulence structure is further analysed using Extended Self Similarity (ESS). A criterion to identify the inertial range and to show the scale independence of the relative exponents is described. Finally, using least-squares fits, the values of some parameters have been obtained which are able to characterize intermittency according to different models.

A note on Kolmogorov's third-order structure-function law, the local isotropy hypothesis and the pressure–velocity correlation

1996 ◽  
Vol 326 ◽  
pp. 343-356 ◽  
Author(s):  
Erik Lindborg
Keyword(s):  
Structure Function ◽  
Strain Tensor ◽  
Inertial Range ◽  
Order Structure ◽  
Two Dimensional ◽  
Mean Flow ◽  
Velocity Correlation ◽  
Third Order ◽  
The Third ◽  
Point Pressure

We show that Kolmogorov's (1941b) inertial-range law for the third-order structure function can be derived from a dynamical equation including pressure terms and mean flow gradient terms. A new inertial-range law, relating the two-point pressure–velocity correlation to the single-point pressure–strain tensor, is also derived. This law shows that the two-point pressure–velocity correlation, just like the third-order structure function, grows linearly with the separation distance in the inertial range. The physical meaning of both this law and Kolmogorov's law is illustrated by a Fourier analysis. An inertial-range law is also derived for the third-order velocity–enstrophy structure function of two-dimensional turbulence. It is suggested that the second-order vorticity structure function of two-dimensional turbulence is constant and scales with$\epsilon ^{2/3}_\omega$in the enstrophy inertial range, εωbeing the enstrophy dissipation. Owing to the constancy of this law, it does not imply a Fourier-space inertial-range law, and therefore it is not equivalent to thek−1law for the enstrophy spectrum, suggested by Kraichnan (1967) and Batchelor (1969).

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