scholarly journals The scaling of straining motions in homogeneous isotropic turbulence

2017 ◽  
Vol 829 ◽  
pp. 31-64 ◽  
Author(s):  
G. E. Elsinga ◽  
T. Ishihara ◽  
M. V. Goudar ◽  
C. B. da Silva ◽  
J. C. R. Hunt
Keyword(s):  
Reynolds Number ◽  
Shear Layer ◽  
Spatial Organization ◽  
Isotropic Turbulence ◽  
Local Strain ◽  
Scale Structure ◽  
Small Scale ◽  
Length Scale ◽  
Local Flow ◽  
Small Scale Structure

The scaling of turbulent motions is investigated by considering the flow in the eigenframe of the local strain-rate tensor. The flow patterns in this frame of reference are evaluated using existing direct numerical simulations of homogeneous isotropic turbulence over a Reynolds number range from $Re_{\unicode[STIX]{x1D706}}=34.6$ up to 1131, and also with reference to data for inhomogeneous, anisotropic wall turbulence. The average flow in the eigenframe reveals a shear layer structure containing tube-like vortices and a dissipation sheet, whose dimensions scale with the Kolmogorov length scale, $\unicode[STIX]{x1D702}$. The vorticity stretching motions scale with the Taylor length scale, $\unicode[STIX]{x1D706}_{T}$, while the flow outside the shear layer scales with the integral length scale, $L$. Furthermore, the spatial organization of the vortices and the dissipation sheet defines a characteristic small-scale structure. The overall size of this characteristic small-scale structure is $120\unicode[STIX]{x1D702}$ in all directions based on the coherence length of the vorticity. This is considerably larger than the typical size of individual vortices, and reflects the importance of spatial organization at the small scales. Comparing the overall size of the characteristic small-scale structure with the largest flow scales and the vorticity stretching motions on the scale of $4\unicode[STIX]{x1D706}_{T}$ shows that transitions in flow structure occur where $Re_{\unicode[STIX]{x1D706}}\approx 45$ and 250. Below these respective transitional Reynolds numbers, the small-scale motions and the vorticity stretching motions are progressively less well developed. Scale interactions are examined by decomposing the average shear layer into a local flow, which is induced by the shear layer vorticity, and a non-local flow, which represents the environment of the characteristic small-scale structure. The non-local strain is $4\unicode[STIX]{x1D706}_{T}$ in width and height, which is consistent with observations in high Reynolds number flow of a $4\unicode[STIX]{x1D706}_{T}$ wide instantaneous shear layer with many $\unicode[STIX]{x1D702}$-scale vortical structures inside (Ishihara et al., Flow Turbul. Combust., vol. 91, 2013, pp. 895–929). In the average shear layer, vorticity aligns with the intermediate principal strain at small scales, while it aligns with the most stretching principal strain at larger scales, consistent with instantaneous turbulence. The length scale at which the alignment changes depends on the Reynolds number. When conditioning the flow in the eigenframe on extreme dissipation, the velocity is strongly affected over large distances. Moreover, the associated peak velocity remains Reynolds number dependent when normalized by the Kolmogorov velocity scale. It signifies that extreme dissipation is not simply a small-scale property, but is associated with large scales at the same time.

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.

On the universality of local dissipation scales in turbulent channel flow

2015 ◽  
Vol 786 ◽  
pp. 234-252 ◽  
Author(s):  
S. C. C. Bailey ◽  
B. M. Witte
Keyword(s):  
Reynolds Number ◽  
Channel Flow ◽  
Large Scale ◽  
Isotropic Turbulence ◽  
Turbulent Channel Flow ◽  
Reynolds Numbers ◽  
Small Scale ◽  
Length Scale ◽  
Scaling Behaviour ◽  
Sixth Moment

Well-resolved measurements of the small-scale dissipation statistics within turbulent channel flow are reported for a range of Reynolds numbers from $Re_{{\it\tau}}\approx 500$ to 4000. In this flow, the local large-scale Reynolds number based on the longitudinal integral length scale is found to poorly describe the Reynolds number dependence of the small-scale statistics. When a length scale based on Townsend’s attached-eddy hypothesis is used to define the local large-scale Reynolds number, the Reynolds number scaling behaviour was found to be more consistent with that observed in homogeneous, isotropic turbulence. The Reynolds number scaling of the dissipation moments up to the sixth moment was examined and the results were found to be in good agreement with predicted scaling behaviour (Schumacher et al., Proc. Natl Acad. Sci. USA, vol. 111, 2014, pp. 10961–10965). The probability density functions of the local dissipation scales (Yakhot, Physica D, vol. 215 (2), 2006, pp. 166–174) were also determined and, when the revised local large-scale Reynolds number is used for normalization, provide support for the existence of a universal distribution which scales differently for inner and outer regions.

Effect of external turbulence on the evolution of a wake in stratified and unstratified environments

2015 ◽  
Vol 772 ◽  
pp. 361-385 ◽  
Author(s):  
Anikesh Pal ◽  
Sutanu Sarkar
Keyword(s):  
Reynolds Number ◽  
Spatial Organization ◽  
Isotropic Turbulence ◽  
Free Stream ◽  
Vertical Direction ◽  
Integral Length Scale ◽  
Moderate Intensity ◽  
Length Scale ◽  
Wake Turbulence ◽  
External Turbulence

Direct numerical simulations are performed to study the evolution of a towed stratified wake subject to external turbulence in the background. A field of isotropic turbulence is combined with an initial turbulent wake field and the combined wake is simulated in a temporally evolving framework similar to that of Rind & Castro (J. Fluid Mech., vol. 710, 2012a, p. 482). Simulations are performed for external turbulence whose initial level varies between zero and a moderate intensity of up to 7 % relative to the free stream and whose initial integral length scale is of the same order as that of the wake turbulence. A series of simulations are carried out at a Reynolds number of 10 000 and Froude number of 3. Background turbulence, especially at a level of 3 % or above, is found to have substantial quantitative effects in the stratified simulations. Turbulence inside the wake increases due to the entrainment of external turbulence, and the energy transfer through turbulent production from mean to fluctuating velocity also increases, leading to reduced mean velocity. The profiles of normalized mean and turbulence quantities in the stratified wake exhibit little change in the vertical direction but the horizontal spread increases in comparison to the case with undisturbed background. The spatial organization of the internal wave field is disrupted even at the 1 % level of external turbulence. However, key characteristics of stratified wakes such as the formation of coherent pancake vortices and the long lifetime of the mean wake are robust to the presence of fluctuations in the background. A corresponding series of simulations for the unstratified situation is carried out at the same Reynolds number of 10 000 and with similar levels of external turbulence. The change of mean and turbulence statistics is found to be weaker in the unstratified cases compared with the corresponding stratified cases and also weaker relative to that found by Rind & Castro (J. Fluid Mech., vol. 710, 2012a, p. 482) at a similar level of external turbulence relative to the free stream and similar integral length scale. Theoretical arguments and additional simulations are provided to show that the level of external turbulence relative to wake turbulence (dissimilar between the present investigation and Rind & Castro (J. Fluid Mech., vol. 710, 2012a, p. 482)) is a key governing parameter in both stratified and unstratified backgrounds.

scholarly journals A Search for Very Compact Structure in 17 OH Masers

1988 ◽  
Vol 129 ◽  
pp. 255-256
Author(s):  
A. J. Kemball ◽  
P. J. Diamond ◽  
F. Mantovani
Keyword(s):  
Galactic Disk ◽  
Hii Regions ◽  
Scale Structure ◽  
Small Scale ◽  
Compact Structure ◽  
Small Scale Structure ◽  
Interstellar Scattering

The apparent spot sizes of OH masers appear to be significantly broadened when seen through the inner galaxy or large extents of the galactic disk (Burke 1968). Bowers et al (1980) found evidence of small-scale structure (≲ 50 mas) in OH sources at distances of less than 5 kpc but this was characteristically absent in very distant sources (≳ 8kpc) at galactic longitudes 1 ≲ 40°. This result is typically explained in terms of interstellar scattering (ISS) by intervening diffuse HII regions.

Analysis of the small-scale structure of turbulence on smooth and rough walls

2003 ◽  
Vol 15 (1) ◽  
pp. 35-46 ◽  
Author(s):  
D. Poggi ◽  
A. Porporato ◽  
L. Ridolfi
Keyword(s):  
Scale Structure ◽  
Small Scale ◽  
Small Scale Structure ◽  
Rough Walls
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