scholarly journals Reynolds-number dependence of the dimensionless dissipation rate in homogeneous magnetohydrodynamic turbulence

2017 ◽  
Vol 95 (1) ◽  
Author(s):  
Moritz Linkmann ◽  
Arjun Berera ◽  
Erin E. Goldstraw
Keyword(s):  
Reynolds Number ◽  
Dissipation Rate ◽  
Magnetohydrodynamic Turbulence ◽  
Reynolds Number Dependence

Scaling of global properties of turbulence and skin friction in pipe and channel flows

2010 ◽  
Vol 652 ◽  
pp. 65-73 ◽  
Author(s):  
VICTOR YAKHOT ◽  
SEAN C. C. BAILEY ◽  
ALEXANDER J. SMITS
Keyword(s):  
Experimental Data ◽  
Reynolds Number ◽  
Kinetic Energy ◽  
Friction Factor ◽  
Turbulent Kinetic Energy ◽  
Dissipation Rate ◽  
Friction Velocity ◽  
Scaling Law ◽  
Global Properties ◽  
Reynolds Number Dependence

Experimental data on the Reynolds number dependence of the area-averaged turbulent kinetic energy K and dissipation rate ℰ are presented. It is shown that while in the interval ReD > 105 the total kinetic energy scales with friction velocity (K/u*2 = const), a new scaling law K/〈U〉2 ∝ K/(u*2ReDθ) = const (θ ≈ 1/4) has been discovered in the interval ReD < 105. It is argued that this transition is responsible for the well-known change in the scaling behaviour of the friction factor observed in pipe and channels flows at ReD ≈ 105.

scholarly journals Reynolds number dependence of Lyapunov exponents of turbulence and fluid particles

2021 ◽  
Vol 103 (3) ◽  
Author(s):  
Itzhak Fouxon ◽  
Joshua Feinberg ◽  
Petri Käpylä ◽  
Michael Mond
Keyword(s):  
Reynolds Number ◽  
Lyapunov Exponents ◽  
Fluid Particles ◽  
Reynolds Number Dependence

Reynolds number dependence of turbulence statistics in the wake of wind turbines

Wind Energy ◽  
2011 ◽  
Vol 15 (5) ◽  
pp. 733-742 ◽  
Author(s):  
Leonardo P. Chamorro ◽  
R.E.A Arndt ◽  
F. Sotiropoulos
Keyword(s):  
Reynolds Number ◽  
Wind Turbines ◽  
Turbulence Statistics ◽  
Reynolds Number Dependence

Contribution towards a Reynolds-stress closure for low-Reynolds-number turbulence

1976 ◽  
Vol 74 (4) ◽  
pp. 593-610 ◽  
Author(s):  
K. Hanjalić ◽  
B. E. Launder
Keyword(s):  
Reynolds Number ◽  
Shear Stress ◽  
Reynolds Stress ◽  
Dissipation Rate ◽  
Numerical Solutions ◽  
Low Reynolds Number ◽  
Transport Processes ◽  
Turbulent Shear ◽  
Turbulent Shear Stress ◽  
Low Reynolds

The problem of closing the Reynolds-stress and dissipation-rate equations at low Reynolds numbers is considered, specific forms being suggested for the direct effects of viscosity on the various transport processes. By noting that the correlation coefficient$\overline{uv^2}/\overline{u^2}\overline{v^2} $is nearly constant over a considerable portion of the low-Reynolds-number region adjacent to a wall the closure is simplified to one requiring the solution of approximated transport equations for only the turbulent shear stress, the turbulent kinetic energy and the energy dissipation rate. Numerical solutions are presented for turbulent channel flow and sink flows at low Reynolds number as well as a case of a severely accelerated boundary layer in which the turbulent shear stress becomes negligible compared with the viscous stresses. Agreement with experiment is generally encouraging.

Reynolds-number dependence of line and surface stretching in turbulence: folding effects

2007 ◽  
Vol 586 ◽  
pp. 59-81 ◽  
Author(s):  
SUSUMU GOTO ◽  
SHIGEO KIDA
Keyword(s):  
Reynolds Number ◽  
Time Scale ◽  
Isotropic Turbulence ◽  
Three Dimensional ◽  
Turnover Time ◽  
Material Object ◽  
Material Objects ◽  
Short Time Scale ◽  
Kolmogorov Scale ◽  
Reynolds Number Dependence

The stretching rate, normalized by the reciprocal of the Kolmogorov time, of sufficiently extended material lines and surfaces in statistically stationary homogeneous isotropic turbulence depends on the Reynolds number, in contrast to the conventional picture that the statistics of material object deformation are determined solely by the Kolmogorov-scale eddies. This Reynolds-number dependence of the stretching rate of sufficiently extended material objects is numerically verified both in two- and three-dimensional turbulence, although the normalized stretching rate of infinitesimal material objects is confirmed to be independent of the Reynolds number. These numerical results can be understood from the following three facts. First, the exponentially rapid stretching brings about rapid multiple folding of finite-sized material objects, but no folding takes place for infinitesimal objects. Secondly, since the local degree of folding is positively correlated with the local stretching rate and it is non-uniformly distributed over finite-sized objects, the folding enhances the stretching rate of the finite-sized objects. Thirdly, the stretching of infinitesimal fractions of material objects is governed by the Kolmogorov-scale eddies, whereas the folding of a finite-sized material object is governed by all eddies smaller than the spatial extent of the objects. In other words, the time scale of stretching of infinitesimal fractions of material objects is proportional to the Kolmogorov time, whereas that of folding of sufficiently extended material objects can be as long as the turnover time of the largest eddies. The combination of the short time scale of stretching of infinitesimal fractions and the long time scale of folding of the whole object yields the Reynolds-number dependence. Movies are available with the online version of the paper.

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 an orifice plate

2013 ◽  
Vol 30 ◽  
pp. 123-132 ◽  
Author(s):  
Oliver Büker ◽  
Peter Lau ◽  
Karsten Tawackolian
Keyword(s):  
Reynolds Number ◽  
Orifice Plate ◽  
Reynolds Number Dependence
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