scholarly journals Experimental study of the influence of anisotropy on the inertial scales of turbulence

2012 ◽  
Vol 692 ◽  
pp. 464-481 ◽  
Author(s):  
Kelken Chang ◽  
Gregory P. Bewley ◽  
Eberhard Bodenschatz

AbstractWe ask whether the scaling exponents or the Kolmogorov constants depend on the anisotropy of the velocity fluctuations in a turbulent flow with no shear. According to our experiment, the answer is no for the Eulerian second-order transverse velocity structure function. The experiment consisted of 32 loudspeaker-driven jets pointed toward the centre of a spherical chamber. We generated anisotropy by controlling the strengths of the jets. We found that the form of the anisotropy of the velocity fluctuations was the same as that in the strength of the jets. We then varied the anisotropy, as measured by the ratio of axial to radial root-mean-square (r.m.s.) velocity fluctuations, between 0.6 and 2.3. The Reynolds number was approximately constant at around ${R}_{\lambda } = 481$. In a central volume with a radius of 50 mm, the turbulence was approximately homogeneous, axisymmetric, and had no shear and no mean flow. We observed that the scaling exponent of the structure function was $0. 70\pm 0. 03$, independent of the anisotropy and regardless of the direction in which we measured it. The Kolmogorov constant, ${C}_{2} $, was also independent of direction and anisotropy to within the experimental error of 4 %.

2008 ◽  
Vol 15 (6) ◽  
pp. 915-929 ◽  
Author(s):  
J. M. Vindel ◽  
C. Yagüe ◽  
J. M. Redondo

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.


Fractals ◽  
2018 ◽  
Vol 26 (04) ◽  
pp. 1850070
Author(s):  
G. C. LAYEK ◽  
SUNITA

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].


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

2006 ◽  
Vol 2 (S237) ◽  
pp. 9-16
Author(s):  
Mark H. Heyer ◽  
Chris Brunt

AbstractThe observational record of turbulence within the molecular gas phase of the interstellar medium is summarized. We briefly review the analysis methods used to recover the velocity structure function from spectroscopic imaging and the application of these tools on sets of cloud data. These studies identify a near-invariant velocity structure function that is independent of the local environment and star formation activity. Such universality accounts for the cloud-to-cloud scaling law between the global line-width and size of molecular clouds found by Larson (1981) and constrains the degree to which supersonic turbulence can regulate star formation. In addition, the evidence for large scale driving sources necessary to sustain supersonic flows is summarized.


2017 ◽  
Vol 820 ◽  
pp. 341-369 ◽  
Author(s):  
S. L. Tang ◽  
R. A. Antonia ◽  
L. Djenidi ◽  
L. Danaila ◽  
Y. Zhou

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.


2008 ◽  
Vol 26 (9) ◽  
pp. 2657-2672 ◽  
Author(s):  
M. L. Parkinson

Abstract. The temporal scaling properties of F-region velocity fluctuations, δvlos, were characterised over 17 octaves of temporal scale from τ=1 s to <1 day using a new data base of 1-s time resolution SuperDARN radar measurements. After quality control, 2.9 (1.9) million fluctuations were recorded during 31.5 (40.4) days of discretionary mode soundings using the Tasmanian (New Zealand) radars. If the fluctuations were statistically self-similar, the probability density functions (PDFs) of δvlos would collapse onto the same PDF using the scaling Ps (δvs, τ)=ταP (δvlos, τ) and δvs=δvlosτ−α where α is the scaling exponent. The variations in scaling exponents α and multi-fractal behaviour were estimated using peak scaling and generalised structure function (GSF) analyses, and a new method based upon minimising the differences between re-scaled probability density functions (PDFs). The efficiency of this method enabled calculation of "α spectra", the temporal spectra of scaling exponents from τ=1 s to ~2048 s. The large number of samples enabled calculation of α spectra for data separated into 2-h bins of MLT as well as two main physical regimes: Population A echoes with Doppler spectral width <75 m s−1 concentrated on closed field lines, and Population B echoes with spectral width >150 m s−1 concentrated on open field lines. For all data there was a scaling break at τ~10 s and the similarity of the fluctuations beneath this scale may be related to the large spatial averaging (~100 km×45 km) employed by SuperDARN radars. For Tasmania Population B, the velocity fluctuations exhibited approximately mono fractal power law scaling between τ~8 s and 2048 s (34 min), and probably up to several hours. The scaling exponents were generally less than that expected for basic MHD turbulence (α=0.25), except close to magnetic dusk where they peaked towards the basic MHD value. For Population A, the scaling exponents were larger than for Population B, having values generally in the range expected for basic MHD and Kolmogorov turbulence (α=0.25–0.33). The α spectra exhibited complicated variations with MLT and τ which must be related to different physical processes exerting more or less influence.


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