Reynolds-number dependence of turbulent velocity and pressure increments

2001 ◽  
Vol 444 ◽  
pp. 343-382 ◽  
Author(s):  
B. R. PEARSON ◽  
R. A. ANTONIA
Keyword(s):  
Reynolds Number ◽  
Fourth Order ◽  
Transverse Velocity ◽  
Inertial Range ◽  
Integral Length Scale ◽  
Length Scale ◽  
Scaling Exponents ◽  
Velocity Increments ◽  
The Mean ◽  
Reynolds Number Dependence

The main focus is the Reynolds number dependence of Kolmogorov normalized low-order moments of longitudinal and transverse velocity increments. The velocity increments are obtained in a large number of flows and over a wide range (40–4250) of the Taylor microscale Reynolds number Rλ. The Rλ dependence is examined for values of the separation, r, in the dissipative range, inertial range and in excess of the integral length scale. In each range, the Kolmogorov-normalized moments of longitudinal and transverse velocity increments increase with Rλ. The scaling exponents of both longitudinal and transverse velocity increments increase with Rλ, the increase being more significant for the latter than the former. As Rλ increases, the inequality between scaling exponents of longitudinal and transverse velocity increments diminishes, reflecting a reduced influence from the large-scale anisotropy or the mean shear on inertial range scales. At sufficiently large Rλ, inertial range exponents for the second-order moment of the pressure increment follow more closely those for the fourth-order moments of transverse velocity increments than the fourth-order moments of longitudinal velocity increments. Comparison with DNS data indicates that the magnitude and Rλ dependence of the mean square pressure gradient, based on the joint-Gaussian approximation, is incorrect. The validity of this approximation improves as r increases; when r exceeds the integral length scale, the Rλ dependence of the second-order pressure structure functions is in reasonable agreement with the result originally given by Batchelor (1951).

Mixed velocity–passive scalar statistics in high-Reynolds-number turbulence

2003 ◽  
Vol 475 ◽  
pp. 173-203 ◽  
Author(s):  
L. MYDLARSKI
Keyword(s):  
Reynolds Number ◽  
Transverse Velocity ◽  
Reynolds Numbers ◽  
Passive Scalar ◽  
Inertial Range ◽  
Scaling Exponents ◽  
Local Isotropy ◽  
Exponential Tails ◽  
Reynolds Number Dependence ◽  
Scalar Fluctuation

Statistics of the mixed velocity–passive scalar field and its Reynolds number dependence are studied in quasi-isotropic decaying grid turbulence with an imposed mean temperature gradient. The turbulent Reynolds number (using the Taylor microscale as the length scale), Rλ, is varied over the range 85 [les ] Rλ [les ] 582. The passive scalar under consideration is temperature in air. The turbulence is generated by means of an active grid and the temperature fluctuations result from the action of the turbulence on the mean temperature gradient. The latter is created by differentially heating elements at the entrance to the wind tunnel plenum chamber. The mixed velocity–passive scalar field evolves slowly with Reynolds number. Inertial-range scaling exponents of the co-spectra of transverse velocity and temperature, Evθ(k1), and its real-space analogue, the ‘heat flux structure function,’ 〈Δv(r)Δθ(r)〉, show a slow evolution towards their theoretical predictions of −7/3 and 4/3, respectively. The sixth-order longitudinal mixed structure functions, 〈(Δu(r))2(Δθ(r))4〉, exhibit inertial-range structure function exponents of 1.36–1.52. However, discrepancies still exist with respect to the various methods used to estimate the scaling exponents, the value of the scalar intermittency exponent, μθ, and the effects of large-scale phenomena (namely shear, decay and turbulent production of 〈θ2〉) on 〈(Δu(r))2(Δθ(r))4〉. All the measured fine-scale statistics required to be zero in a locally isotropic flow are, or tend towards, zero in the limit of large Reynolds numbers. The probability density functions (PDFs) of Δv(r)Δθ(r) exhibit roughly exponential tails for large separations and super-exponential tails for small separations, thus displaying the effects of internal intermittency. As the Reynolds number increases, the PDFs become symmetric at the smallest scales – in accordance with local isotropy. The expectation of the transverse velocity fluctuation conditioned on the scalar fluctuation is linear for all Reynolds numbers, with slope equal to the correlation coefficient between v and θ. The expectation of (a surrogate of) the Laplacian of the scalar reveals a Reynolds number dependence when conditioned on the transverse velocity fluctuation (but displays no such dependence when conditioned on the scalar fluctuation). This former Reynolds number dependence is consistent with Taylor’s diffusivity independence hypothesis. Lastly, for the statistics measured, no violations of local isotropy were observed.

Reynolds number dependence of the small-scale structure of grid turbulence

2000 ◽  
Vol 406 ◽  
pp. 81-107 ◽  
Author(s):  
T. ZHOU ◽  
R. A. ANTONIA
Keyword(s):  
Reynolds Number ◽  
Power Law ◽  
Fourth Order ◽  
Transverse Velocity ◽  
Scale Structure ◽  
Small Scale ◽  
Grid Turbulence ◽  
Small Scale Structure ◽  
Velocity Increments ◽  
The Difference

The small-scale structure of grid turbulence is studied primarily using data obtained with a transverse vorticity (ω3) probe for values of the Taylor-microscale Reynolds number Rλ in the range 27–100. The measured spectra of the transverse vorticity component agree within ±10% with those calculated using the isotropic relation over nearly all wavenumbers. Scaling-range exponents of transverse velocity increments are appreciably smaller than exponents of longitudinal velocity increments. Only a small fraction of this difference can be attributed to the difference in intermittency between the locally averaged energy dissipation rate and enstrophy fluctuations. The anisotropy of turbulence structures in the scaling range, which reflects the small values of Rλ, is more likely to account for most of the difference. All four fourth-order rotational invariants Iα (α = 1 to 4) proposed by Siggia (1981) were evaluated. For any particular value of α, the magnitude of the ratio Iα / I1 is approximately constant, independently of Rλ. The implication is that the invariants are interdependent, at least in isotropic and quasi-Gaussian turbulence, so that only one power-law exponent may be sufficient to describe the Rλ dependence of all fourth-order velocity derivative moments in this type of flow. This contrasts with previous suggestions that at least two power-law exponents are needed, one for the rate of strain and the other for vorticity.

Reynolds number dependence of the mean flow in a circular pipe

1997 ◽  
Author(s):  
M. Zagarola ◽  
A. Smits ◽  
M. Zagarola ◽  
A. Smits
Keyword(s):  
Reynolds Number ◽  
Circular Pipe ◽  
Mean Flow ◽  
The Mean ◽  
Reynolds Number Dependence

Analogy between predictions of Kolmogorov and Yaglom

1997 ◽  
Vol 332 ◽  
pp. 395-409 ◽  
Author(s):  
R. A. Antonia ◽  
M. Ould-Rouis ◽  
F. Anselmet ◽  
Y. Zhu
Keyword(s):  
Reynolds Number ◽  
Prandtl Number ◽  
Longitudinal Velocity ◽  
Turbulent Wake ◽  
Mean Value ◽  
Order Moment ◽  
Third Order ◽  
The Third ◽  
Velocity Increments ◽  
The Mean

The relation, first written by Kolmogorov, between the third-order moment of the longitudinal velocity increment δu1 and the second-order moment of δu1 is presented in a slightly more general form relating the mean value of the product δu1(δui)2, where (δui)2 is the sum of the square of the three velocity increments, to the secondorder moment of δui. In this form, the relation is similar to that derived by Yaglom for the mean value of the product δu1(δuθ)2 where (δuθ)2 is the square of the temperature increment. Both equations reduce to a ‘four-thirds’ relation for inertialrange separations and differ only through the appearance of the molecular Prandtl number for very small separations. These results are confirmed by experiments in a turbulent wake, albeit at relatively small values of the turbulence Reynolds number.

Lateral dispersion in random cylinder arrays at high Reynolds number

2008 ◽  
Vol 600 ◽  
pp. 339-371 ◽  
Author(s):  
YUKIE TANINO ◽  
HEIDI M. NEPF
Keyword(s):  
Turbulence Intensity ◽  
Turbulent Diffusion ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Laboratory Data ◽  
Integral Length Scale ◽  
Length Scale ◽  
Linear Superposition ◽  
Cylinder Diameter ◽  
The Mean

Laser-induced fluorescence was used to measure the lateral dispersion of passive solute in random arrays of rigid, emergent cylinders of solid volume fraction φ=0.010–0.35. Such densities correspond to those observed in aquatic plant canopies and complement those in packed beds of spheres, where φ≥0.5. This paper focuses on pore Reynolds numbers greater than Res=250, for which our laboratory experiments demonstrate that the spatially averaged turbulence intensity and Kyy/(Upd), the lateral dispersion coefficient normalized by the mean velocity in the fluid volume, Up, and the cylinder diameter, d, are independent of Res. First, Kyy/(Upd) increases rapidly with φ from φ =0 to φ=0.031. Then, Kyy/(Upd) decreases from φ=0.031 to φ=0.20. Finally, Kyy/(Upd) increases again, more gradually, from φ=0.20 to φ=0.35. These observations are accurately described by the linear superposition of the proposed model of turbulent diffusion and existing models of dispersion due to the spatially heterogeneous velocity field that arises from the presence of the cylinders. The contribution from turbulent diffusion scales with the mean turbulence intensity, the characteristic length scale of turbulent mixing and the effective porosity. From a balance between the production of turbulent kinetic energy by the cylinder wakes and its viscous dissipation, the mean turbulence intensity for a given cylinder diameter and cylinder density is predicted to be a function of the form drag coefficient and the integral length scale lt. We propose and experimentally verify that lt=min{d, 〈sn〉A}, where 〈sn〉A is the average surface-to-surface distance between a cylinder in the array and its nearest neighbour. We farther propose that only turbulent eddies with mixing length scale greater than d contribute significantly to net lateral dispersion, and that neighbouring cylinder centres must be farther than r* from each other for the pore space between them to contain such eddies. If the integral length scale and the length scale for mixing are equal, then r*=2d. Our laboratory data agree well with predictions based on this definition of r*.

Three-component vorticity measurements in a turbulent grid flow

1998 ◽  
Vol 374 ◽  
pp. 29-57 ◽  
Author(s):  
R. A. ANTONIA ◽  
T. ZHOU ◽  
Y. ZHU
Keyword(s):  
Energy Dissipation ◽  
Dissipation Rate ◽  
Velocity Structure ◽  
Transverse Velocity ◽  
Longitudinal Velocity ◽  
Energy Dissipation Rate ◽  
Grid Turbulence ◽  
Local Isotropy ◽  
Velocity Increments ◽  
The Mean

All components of the fluctuating vorticity vector have been measured in decaying grid turbulence using a vorticity probe of relatively simple geometry (four X-probes, i.e. a total of eight hot wires). The data indicate that local isotropy is more closely satisfied than global isotropy, the r.m.s. vorticities being more nearly equal than the r.m.s. velocities. Two checks indicate that the performance of the probe is satisfactory. Firstly, the fully measured mean energy dissipation rate 〈ε〉 is in good agreement with the value inferred from the rate of decay of the mean turbulent energy 〈q2〉 in the quasi-homogeneous region; the isotropic mean energy dissipation rate 〈εiso〉 agrees closely with this value even though individual elements of 〈ε〉 indicate departures from isotropy. Secondly, the measured decay rate of the mean-square vorticity 〈ω2〉 is consistent with that of 〈q2〉 and in reasonable agreement with the isotropic form of the transport equation for 〈ω2〉. Although 〈ε〉≃〈εiso〉, there are discernible differences between the statistics of ε and εiso; in particular, εiso is poorly correlated with either ε or ω2. The behaviour of velocity increments has been examined over a narrow range of separations for which the third-order longitudinal velocity structure function is approximately linear. In this range, transverse velocity increments show larger departures than longitudinal increments from predictions of Kolmogorov (1941). The data indicate that this discrepancy is only partly associated with differences between statistics of locally averaged ε and ω2, the latter remaining more intermittent than the former across this range. It is more likely caused by a departure from isotropy due to the small value of Rλ, the Taylor microscale Reynolds number, in this experiment.

A measure of scale-dependent asymmetry in turbulent boundary layer flows: scaling and Reynolds number similarity

2016 ◽  
Vol 797 ◽  
pp. 549-563 ◽  
Author(s):  
Arvind Singh ◽  
Kevin B. Howard ◽  
Michele Guala
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Energy Transfer ◽  
Turbulent Boundary Layer ◽  
Inertial Range ◽  
Wall Region ◽  
Local Energy ◽  
Boundary Layer Flows ◽  
Non Local ◽  
Velocity Increments

The distribution of temporal scale-dependent streamwise velocity increments is investigated in turbulent boundary layer flows at laboratory and atmospheric Reynolds numbers, using the St. Anthony Falls Laboratory wind tunnel and the Surface Layer Turbulence and Environmental Science Test dataset, respectively. The third-order moments of velocity increments, or asymmetry index $A(a,z)$, is computed for varying wall distance $z$ and time scale separation $a$, where it was observed to leave a robust, distinct signature in the form of a hump, independent of Reynolds number and located across the inertial range. The hump is observed in wall region limited to $z^{+}<5\times 10^{3}$, with a tendency to shift towards smaller time scales as the surface is approached ($z^{+}<70$). Comparing the two datasets, the hump, and its location, are found to obey inner wall scaling and is regarded as a genuine feature of the canonical turbulent boundary layer. The magnitude cumulant analysis of the scale-dependent velocity increments further reveals that intermittency is also enhanced near the wall, in the same flow region where the asymmetry signature was observed. The combination of asymmetry and intermittency is inferred to point at non-local energy transfer and scale coupling across a range of scales. From a turbulent structure perspective, such non-local energy transfer can be seen as the result of strong scale-interaction processes between outer scale motions in the logarithmic layer impacting and distorting smaller scales at the wall, through abrupt energy transfer across scales bypassing the typical energy cascade of the inertial range.

Whole Process Wind Characteristics Field Measurements of a Strong Wind

2011 ◽  
Vol 243-249 ◽  
pp. 5094-5100 ◽  
Author(s):  
Ke Yang ◽  
Wen Hai Shi ◽  
Zheng Nong Li
Keyword(s):  
Wind Speed ◽  
Turbulence Intensity ◽  
Field Measurements ◽  
Integral Length Scale ◽  
Length Scale ◽  
Strong Wind ◽  
Gust Factor ◽  
Mean Wind Speed ◽  
Wind Characteristics ◽  
The Mean

This paper presents field measurement results of boundary layer wind characteristics over typical open country during the passages of typhoon Fung-wong passed by Wenzhou in July 2008. The field data such as wind speed and wind direction were measured from two propeller anemometers placed at the height of about 30m. The measured wind data are analyzed to obtain the information on mean wind speed and direction, turbulence intensity, gust factor, turbulence integral length scale and spectra of wind speed fluctuations. The results clearly demonstrate that the turbulence intensity and gust factor of typhoon Fung-wong are larger than normal, and there is a tendency for the turbulence intensities to decrease with the increase of the mean wind speed, however, there is another tendency for the turbulence integral length scale to increase with the increase of the mean wind speed. The power spectral densities of fluctuating wind speed in longitudinal and lateral directions obtained from the measured wind speed data roughly fit with Von Karman spectra. The results presented in this paper are expected to be of use to researchers and engineers involved in design of low-rise buildings.

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