A Closure for Isotropic Turbulence Based on Extended Scale Similarity Theory in Physical Space

2018 ◽  
Vol 35 (8) ◽  
pp. 080501
Author(s):  
Chu-Han Wang ◽  
Le Fang
Keyword(s):  
Isotropic Turbulence ◽  
Similarity Theory ◽  
Physical Space ◽  
Scale Similarity ◽  
Extended Scale

Vorticity and passive-scalar dynamics in two-dimensional turbulence

1987 ◽  
Vol 183 ◽  
pp. 379-397 ◽  
Author(s):  
Armando Babiano ◽  
Claude Basdevant ◽  
Bernard Legras ◽  
Robert Sadourny
Keyword(s):  
Similarity Theory ◽  
Physical Space ◽  
Passive Scalar ◽  
Inertial Range ◽  
Flow Dynamics ◽  
Two Dimensional ◽  
Closure Model ◽  
Coherent Vortices ◽  
Vorticity Transport ◽  
Kolmogorov Theory

The dynamics of vorticity in two-dimensional turbulence is studied by means of semi-direct numerical simulations, in parallel with passive-scalar dynamics. It is shown that a passive scalar forced and dissipated in the same conditions as vorticity, has a quite different behaviour. The passive scalar obeys the similarity theory à la Kolmogorov, while the enstrophy spectrum is much steeper, owing to a hierarchy of strong coherent vortices. The condensation of vorticity into such vortices depends critically both on the existence of an energy invariant (intimately related to the feedback of vorticity transport on velocity, absent in passive-scalar dynamics, and neglected in the Kolmogorov theory of the enstrophy inertial range); and on the localness of flow dynamics in physical space (again not considered by the Kolmogorov theory, and not accessible to closure model simulations). When space localness is artificially destroyed, the enstrophy spectrum again obeys a k−1 law like a passive scalar. In the wavenumber range accessible to our experiments, two-dimensional turbulence can be described as a hierarchy of strong coherent vortices superimposed on a weak vorticity continuum which behaves like a passive scalar.

Evidence for scale similarity of internal intermittency in turbulent flows at large Reynolds numbers

1975 ◽  
Vol 71 (3) ◽  
pp. 417-440 ◽  
Author(s):  
C. W. Van Atta ◽  
T. T. Yeh
Keyword(s):  
Turbulent Flows ◽  
Similarity Theory ◽  
Sampling Rate ◽  
Streamwise Velocity ◽  
Characteristic Functions ◽  
Systematic Change ◽  
Turbulent Dissipation ◽  
Taylor’S Hypothesis ◽  
Scale Similarity ◽  
Probability Densities

Some new measurements and a reassessment of previous data on statistical properties of the breakdown coefficients qr,l in high Reynolds number turbulence show the existence of a range of scale similarity for scales larger than those in the viscous range (l [ges ] 36η). The rate of variation of the probability density p(qr,l) with changing outer scale l/η decreases as l/η increases, becoming fairly insignificant for the largest values of l/η. Measurements of characteristic functions of the probability densities show a substantial degree of statistical independence for sequential adjoint values of qr,l, consistent with the small values of the correlation coefficients for these variables. The data for the moments of qr,l exhibit a behaviour very close to that predicted by the scale-similarity theory when only data for r [ges ] 36η are considered, i.e. data for smaller inner length scales are excluded. The moments and corresponding values of the parameters μp are in good agreement with our previous results and with some earlier data of Kholmyansky, but some rather large unresolved differences in the probability densities of qr,l are found on comparing the present data with those of Kholmyansky. The present measurements of breakdown coefficients for ζ1 = [uscr ]− 1∂u/∂t = ∂(In [uscr ])/∂tand ζ2 = U−1∂u/∂t the time derivatives of the streamwise velocity and its logarithm measured in the atmospheric boundary layer, resolve some previous questions concerning the sensitivity of the results obtained to the choice of positive variable, varying sampling rates and the values of external parameters.For low sampling rates, a systematic change in the shape of the probability densities p(qr,l) with varying digital sampling rate is found using either ζ1 or ζ2. For sufficiently high sampling rates, the probability densities are independent of the sampling rate; and invariant results are obtained when the sampling rate is at least one-quarter of the Kolmogorov frequency associated with the viscous length scale based on the turbulent dissipation rate. The probability densities p(qr,l) measured using either ζ1 or ζ2 are very similar to the corresponding spectra of ζ1 or ζ2 respectively. Comparison of the mean-square values of ζ1 and ζ2 with an extended form of Taylor's hypothesis shows that the variable ζ1 is not a good approximation to the true spatial derivative ∂u/∂x, and the use of such an approximation can lead to results that are both qualitatively and quantitatively incorrect.

scholarly journals A similarity theory of locally homogeneous and isotropic turbulence generated by a Smagorinsky-type LES

1996 ◽  
Vol 325 ◽  
pp. 239-260 ◽  
Author(s):  
Andreas Muschinski
Keyword(s):  
Newtonian Fluid ◽  
Material Parameter ◽  
Isotropic Turbulence ◽  
Similarity Theory ◽  
Reynolds Numbers ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Spectral Models ◽  
Homogeneous And Isotropic Turbulence ◽  
Locally Homogeneous

A Kolmogorov-type similarity theory of locally homogeneous and isotropic turbulence generated by a Smagorinsky-type large-eddy simulation (LES) at very large LES Reynolds numbers is developed and discussed. The underlying concept is that the LES equations may be considered equations of motion of specific hypothetical fully turbulent non-Newtonian fluids, called ‘LES fluids’. It is shown that the length scale ls = csδ, which scales the magnitude of the variable viscosity in a Smagorinsky-type LES, is the ‘Smagorinsky-fluid’ counterpart of Kolmogorov's dissipation length $\eta = v^{3/4}\epsilon^{-1/4}$ for a Newtonian fluid where ν is the kinematic viscosity and ε is the energy dissipation rate. While in a Newtonian fluid the viscosity is a material parameter and the length ν depends on ε, in a Smagorinsky fluid the length ls is a material parameter and the viscosity depends on ε. The Smagorinsky coefficient cs may be considered the reciprocal of a ‘microstructure Knudsen number’ of a Smagorinsky fluid. A combination of Lilly's (1967) cut-off model with two well-known spectral models for dissipation-range turbulence (Heisenberg 1948; Pao 1965) leads to models for the LES-generated Kolmogorov coefficient αLES as a function of cs. Both models predict an intrinsic overestimation of αLES for finite values of cs. For cs = 0.2 Heisenberg's and Pao's models provide αLES = 1.74 (16% overestimation) and αLES = 2.14 (43% overestimation), respectively, if limcs → (αLES) = 1.5 is ad hoc assumed. The predicted overestimation becomes negligible beyond about cs = 0.5. The requirement cs > 0.5 is equivalent to Δ < 2ls. A similar requirement, L < 2η where L is the wire length of hot-wire anemometers, has been recommended by experimentalists. The value of limcs → (αLES) for a Smagorinsky-type LES at very large LES Reynolds numbers is not predicted by the models and remains unknown. Two critical values of cs are identified. The first critical cs is Lilly's (1967) value, which indicates the cs below which finite-difference-approximation errors become important; the second critical cs is the value beyond which the Reynolds number similarity is violated.

NEW DEVELOPMENTS AND CLASSICAL THEORIES OF TURBULENCE

1996 ◽  
Vol 10 (18n19) ◽  
pp. 2325-2392 ◽  
Author(s):  
E. LEVICH
Keyword(s):  
Turbulent Flows ◽  
Isotropic Turbulence ◽  
Physical Space ◽  
Phase Coherence ◽  
Navier Stokes ◽  
Homogeneous Isotropic Turbulence ◽  
Navier Stokes Equation ◽  
Inviscid Flows ◽  
Turbulence Control ◽  
Developed Turbulence

In this paper we review certain classical and modern concepts pertinent for the theory of developed turbulent flows. We begin by introducing basic facts concerning the properties of the Navier-Stokes equation with the emphasis on invariant properties of the vorticity field. Then we discuss classical semiempirical approaches to developed turbulence which for a long time have constituted a basis for engineering solutions of turbulent flows problems. We do it for two examples, homogeneous isotropic turbulence and flat channel turbulent flow. Next we discuss the insufficiency of classical semi-empirical approaches. We show that intermittency is an intrinsic feature of all turbulent flows and hence it should be accounted for in any reasonable theoretical approach to turbulence. We argue that intermittency in physical space is in one to one correspondence with certain phase coherence of turbulence in an appropriate dual space, e.g. Fourier space for the case of homogeneous isotropic turbulence. In the same time the phase coherence has its origin in invariant topological properties of vortex lines in inviscid flows, modified by the presence of small molecular viscosity. This viewpoint is expounded again using the examples of homogeneous isotropic turbulence and channel flow turbulence. Finally we briefly discuss the significance of phase coherence and intermittency in turbulence for the fundamental engineering challenge of turbulence control.

Physical-Space Nonlocality in Decaying Isotropic Turbulence

1993 ◽  
Vol 62 (11) ◽  
pp. 3783-3787 ◽  
Author(s):  
Seigo Kishiba ◽  
Koji Ohkitani ◽  
Shigeo Kida
Keyword(s):  
Isotropic Turbulence ◽  
Physical Space
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