A note on the velocity derivative flatness factor in decaying HIT

2017 ◽  
Vol 29 (5) ◽  
pp. 051702 ◽  
Author(s):  
L. Djenidi ◽  
L. Danaila ◽  
R. A. Antonia ◽  
S. Tang
Keyword(s):  
Velocity Derivative ◽  
Flatness Factor

scholarly journals Reynolds number effect on the velocity derivative flatness factor

2018 ◽  
Vol 856 ◽  
pp. 426-443 ◽  
Author(s):  
M. Meldi ◽  
L. Djenidi ◽  
R. Antonia
Keyword(s):  
Reynolds Number ◽  
Isotropic Turbulence ◽  
Nauk Sssr ◽  
Quantitative Agreement ◽  
Homogeneous Isotropic Turbulence ◽  
Simulation Data ◽  
Akad Nauk Sssr ◽  
Analytic Expression ◽  
Velocity Derivative ◽  
Flatness Factor

This paper investigates the effect of a finite Reynolds number (FRN) on the flatness factor ($F$) of the velocity derivative in decaying homogeneous isotropic turbulence by applying the eddy damped quasi-normal Markovian (EDQNM) method to calculate all terms in an analytic expression for $F$ (Djenidi et al., Phys. Fluids, vol. 29 (5), 2017b, 051702). These terms and hence $F$ become constant when the Taylor microscale Reynolds number, $Re_{\unicode[STIX]{x1D706}}$ exceeds approximately $10^{4}$. For smaller values of $Re_{\unicode[STIX]{x1D706}}$, $F$, like the skewness $-S$, increases with $Re_{\unicode[STIX]{x1D706}}$; this behaviour is in quantitative agreement with experimental and direct numerical simulation data. These results indicate that one must first ensure that $Re_{\unicode[STIX]{x1D706}}$ is large enough for the FRN effect to be negligibly small before the hypotheses of Kolmogorov (Dokl. Akad. Nauk SSSR, vol. 30, 1941a, pp. 301–305; Dokl. Akad. Nauk SSSR, vol. 32, 1941b, pp. 16–18; J. Fluid Mech., vol. 13, 1962, pp. 82–85) can be assessed unambiguously. An obvious implication is that results from experiments and direct numerical simulations for which $Re_{\unicode[STIX]{x1D706}}$ is well below $10^{4}$ may not be immune from the FRN effect. Another implication is that a power-law increase of $F$ with respect to $Re_{\unicode[STIX]{x1D706}}$, as suggested by the Kolmogorov 1962 theory, is not tenable when $Re_{\unicode[STIX]{x1D706}}$ is large enough.

Hot-Wire Measurements in a Plane Turbulent Jet

1965 ◽  
Vol 32 (4) ◽  
pp. 721-734 ◽  
Author(s):  
Gunnar Heskestad
Keyword(s):  
Reynolds Number ◽  
Energy Balance ◽  
Turbulent Jet ◽  
Turbulent Intensity ◽  
Turbulent Motion ◽  
Hot Wire ◽  
Reynolds Number Effect ◽  
Mach Numbers ◽  
Velocity Derivative ◽  
Flatness Factor

Results from hot-wire measurements in a plane turbulent jet of air are reported. The jet was found to be approximately self-preserving sufficiently far downstream where measurements of intermittency and data for calculating the energy balance of the turbulent motion were obtained. Measurements were also made of the effect of the jet speed (assumed equivalent to a Reynolds-number effect for the low Mach numbers used) on the centerline development of turbulent intensity and the flatness factor of the velocity derivative at a fixed downstream centerline location.

Lateral vorticity measurements in a turbulent wake

1996 ◽  
Vol 323 ◽  
pp. 173-200 ◽  
Author(s):  
R. A. Antonia ◽  
Y. Zhu ◽  
H. S. Shafi
Keyword(s):  
Velocity Structure ◽  
Streamwise Velocity ◽  
Turbulent Wake ◽  
Lateral Velocity ◽  
Local Isotropy ◽  
Wire Probe ◽  
Spatial Derivatives ◽  
Velocity Derivative ◽  
Derivatives Of ◽  
Flatness Factor

The accurate measurement of vorticity has proven difficult because of the difficulty of estimating spatial derivatives of velocity fluctuations reliably. A method is proposed for correcting the lateral vorticity spectrum measured using a four-wire probe. The attenuation of the measured spectrum increases as the wavenumber increases but does not vanish when the wavenumber is zero. Although the correction procedure assumes local isotropy, the major contributor to the high-wavenumber part of the vorticity spectrum is the streamwise derivative of the lateral velocity fluctuation, and the correction of this latter quantity does not depend on local isotropy. Satisfactory support for local isotropy is provided by the high-wavenumber parts of the velocity, velocity derivative and vorticity spectra measured on the centreline of a turbulent wake. Second- and fourth-order moments of vorticity show departures from local isotropy but the degree of departure seems unaffected by the turbulence Reynolds number Rλ. The vorticity probability density function is approximately exponential and has tails which stretch out to larger amplitudes as Rλ increases. The vorticity flatness factor, which is appreciably larger than the flatness factor of the streamwise velocity derivative, also increases with Rλ. When Rλ is sufficiently large for velocity structure functions to indicate a r2/3 inertial range, two-point longitudinal correlations of lateral vorticity fluctuations give encouraging support for the theoretical r−4/3 behaviour.

Derivative Statistics of Axial Velocity and Passive Scalar in the Jet Diffusion Field of High-Schmidt-Number Matter

2007 ◽  
Author(s):  
Y. Sakai ◽  
K. Uchida ◽  
T. Kubo ◽  
K. Nagata
Keyword(s):  
Axial Velocity ◽  
Schmidt Number ◽  
Water Solution ◽  
Passive Scalar ◽  
Streamwise Velocity ◽  
The Other ◽  
Diffusion Field ◽  
High Schmidt Number ◽  
Velocity Derivative ◽  
Flatness Factor

In this study, a water solution of dye (whose Schmidt number is about 3,800) was issued into the quiescent water as an axisymmetric turbulent jet and the simultaneous measurements of axial velocity and concentration have been performed using the combined probe of I-type hot-film and fiber-optic concentration sensor based on the Lambert-Beer’s law. Then we calculated the PDF (Probability Density Function) for the streamwise velocity derivative ∂u/∂x and streamwise concentration derivative ∂c/∂x. It was confirmed that the PDFs for ∂u/∂x skew negatively, and the values of skewness (S∂u/∂x) and flatness factor (F∂u/∂x) are consistent with the other data (see Sreenivasan and Antonia, 1997). However, with regard to the PDFs for ∂c/∂x, the skewness (S∂c/∂x) show the values very close to zero, unlikely the past other data which show the magnitude of 0.5∼1.0. On the other hand, the flatness factor (F∂c/∂x) show the values of 7.0∼8.0 which are consistent with other data. This result suggests that the fine-scale structure of a high-Schmidt-number diffusion field is almost isotropic although it is intermittent.

The structure of internal intermittency in turbulent flows at large Reynolds number: experiments on scale similarity

1973 ◽  
Vol 59 (3) ◽  
pp. 537-559 ◽  
Author(s):  
C. W. Van Atta ◽  
T. T. Yeh
Keyword(s):  
Reynolds Number ◽  
Probability Density ◽  
Streamwise Velocity ◽  
Statistical Characteristics ◽  
Large Reynolds Number ◽  
Higher Moments ◽  
Scale Similarity ◽  
Probability Densities ◽  
Scale Ratio ◽  
Velocity Derivative

Some of the statistical characteristics of the breakdown coefficient, defined as the ratio of averages over different spatial regions of positive variables characterizing the fine structure and internal intermittency in high Reynolds number turbulence, have been investigated using experimental data for the streamwise velocity derivative ∂u/∂tmeasured in an atmospheric boundary layer. The assumptions and predictions of the hypothesis of scale similarity developed by Novikov and by Gurvich & Yaglom do not adequately describe or predict the statistical characteristics of the breakdown coefficientqr,lof the square of the streamwise velocity derivative. Systematic variations in the measured probability densities and consistent variations in the measured moments show that the assumption that the probability density of the breakdown coefficient is a function only of the scale ratio is not satisfied. The small positive correlation between adjoint values ofqr,land measurements of higher moments indicate that the assumption that the probability densities for adjoint values ofqr,lare statistically independent is also not satisfied. The moments ofqr,ldo not have the simple power-law character that is a consequence of scale similarity.As the scale ratiol/rchanges, the probability density ofqr,levolves from a sharply peaked, highly negatively skewed density for large values of the scale ratio to a very symmetrical distribution when the scale ratio is equal to two, and then to a highly positively skewed density as the scale ratio approaches one. There is a considerable effect of heterogeneity on the values of the higher moments, and a small but measurable effect on the mean value. The moments are roughly symmetrical functions of the displacement of the shorter segment from the centre of the larger one, with a minimum value when the shorter segment is centrally located within the larger one.

The spatial structure and statistical properties of homogeneous turbulence

1991 ◽  
Vol 225 ◽  
pp. 1-20 ◽  
Author(s):  
A. Vincent ◽  
M. Meneguzzi
Keyword(s):  
Numerical Simulation ◽  
Reynolds Number ◽  
Energy Spectrum ◽  
Velocity Structure ◽  
Three Dimensional ◽  
Inertial Subrange ◽  
Integral Scale ◽  
Turbulent Field ◽  
Velocity Derivative ◽  
Non Gaussian

A direct numerical simulation at resolution 2403 is used to obtain a statistically stationary three-dimensional homogeneous and isotropic turbulent field at a Reynolds number around 1000 (Rλ ≈ 150). The energy spectrum displays an inertial subrange. The velocity derivative distribution, known to be strongly non-Gaussian, is found to be close to, but not, exponential. The nth-order moments of this distribution, as well as the velocity structure functions, do not scale with n as predicted by intermittency models. Visualization of the flow confirms the previous finding that the strongest vorticity is organized in very elongated thin tubes. The width of these tubes is of the order of a few dissipation scales, while their length can reach the integral scale of the flow.

Small-scale characteristics of a turbulent boundary layer over a rough wall

1997 ◽  
Vol 342 ◽  
pp. 263-293 ◽  
Author(s):  
H. S. SHAFI ◽  
R. A. ANTONIA
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Outer Layer ◽  
Large Scale ◽  
Energy Dissipation Rate ◽  
Wall Layer ◽  
Rough Wall ◽  
Small Scale ◽  
Smooth Wall ◽  
Velocity Derivative

Measurements of the spanwise and wall-normal components of vorticity and their constituent velocity derivative fluctuations have been made in a turbulent boundary layer over a mesh-screen rough wall using a four-hot-wire vorticity probe. The measured spectra and variances of vorticity and velocity derivatives have been corrected for the effect of spatial resolution. The high-wavenumber behaviour of the spectra conforms closely with isotropy. Over most of the outer layer, the normalized magnitudes of the velocity derivative variances differ significantly from those over a smooth wall layer. The differences are such that the variances are much more nearly isotropic over the rough wall than on the smooth wall. This behaviour is consistent with earlier observations that the large-scale structure in this rough wall layer is more isotropic than that in a smooth wall layer. Isotropy-based approximations for the mean energy dissipation rate and mean enstrophy are consequently more reliable in this rough wall layer than in a smooth wall layer. In the outer layer, the vorticity variances are slightly larger than those over a smooth wall; reflecting structural differences between the two flows.

Sign in / Sign up

Export Citation Format

Share Document