We study velocity derivative skewness S of incompressible homogeneous isotropic turbulence. By using exact relations of isotropic turbulence and various typical models of second-order structure function and energy spectrum it is found that when Taylor-microscale Reynolds number is high. Here, C is a coefficient, is the center wavenumber of energy dissipation spectrum, and is the Kolmogorov wavenumber. Therefore, the problem of Reynolds number dependence of S becomes the problem of Reynolds number dependence of In the inertial range, we have scaling and is the second-order inertial-range scaling exponent. Equality is valid in the case of (intermittency models of Kolmogorov’s 1962 theory) as well as in the case of (Kolmogorov’s 1941 theory).
REFERENCES
1.
C. W.
Van Atta
and R. A.
Antonia
, “Reynolds number dependence of skewness and flatness factors of turbulent velocity derivatives
,” Phys. Fluids
23
, 252
(1980
).2.
M.
Nelkin
, “Universality and scaling in fully developed turbulence
,” Adv. Phys.
43
, 143
(1994
).3.
K. R.
Sreenivasan
and R. A.
Antonia
, “The phenomenology of small-scale turbulence
,” Annu. Rev. Fluid Mech.
29
, 435
(1997
).4.
A. N.
Kolmogorov
, “Local structure of turbulence in an incompressible fluid for very large Renolds number
,” Dokl. Akad. Nauk SSSR
30
, 299
(1941
);A. N.
Kolmogorov
, “A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number
,” J. Fluid Mech.
13
, 82
(1962
);A. S. Monin and A. M. Yaglom, Statistical Fluid Mechanics (Cambridge University Press, Cambridge, 1975);
U. Frisch, Turbulence: The Legacy of A. N. Kolmogorov (Cambridge University Press, Cambridge, 1995).
5.
R. H.
Kraichnan
, “Models of intermittency in hydrodynamic turbulence
,” Phys. Rev. Lett.
65
, 575
(1990
).6.
A.
Vincent
and M.
Meneguzzi
, “The spatial structure and statistical properties of homogeneous turbulence
,” J. Fluid Mech.
225
, 1
(1991
).7.
R.
Betchov
, “An inequality concerning the production of vorticity in isotropic turbulence
,” J. Fluid Mech.
1
, 497
(1956
).8.
J.
Qian
, “A closure theory of intermittency of turbulence
,” Phys. Fluids
29
, 2165
(1986
).9.
S. G.
Saddoughi
and S. V.
Veeravalli
, “Local isotropy in turbulent boundary layer at high Reynolds number
,” J. Fluid Mech.
268
, 333
(1994
).10.
J.
Qian
, “Real and pseudo Kolmogorov constant
,” J. Phys. Soc. Jpn.
62
, 926
(1993
);J.
Qian
, “Experimental values of Kolmogorov constant of turbulence
,” J. Phys. Soc. Jpn.
65
, 2502
(1996
).11.
L.
Sirovich
, L.
Smith
, and V.
Yakhot
, “Energy spectrum of homogeneous and isotropic turbulence in far dissipation range
,” Phys. Rev. Lett.
72
, 344
(1994
).12.
D.
Loshe
and A. M.
Groeling
, “Bottleneck effects in turbulence: Scaling phenomena in r versus p space
,” Phys. Rev. Lett.
74
, 1747
(1995
);S.
Grossmann
, “Asymptotic dissipation rate in turbulence
,” Phys. Rev. E
51
, 6275
(1995
);G.
Stolovitzky
, K. R.
Sreenivasan
, and A.
Juneja
, “Scaling functions and scaling exponents in turbulence
,” Phys. Rev. E
48
, R3217
(1993
);G.
Stolovitzky
and K. R.
Sreenivasan
, “Intermittency the second-order structure function, and the turbulent energy-dissipation rate
,” Phys. Rev. E
52
, 3242
(1995
).13.
J.
Qian
, “Universal equilibrium range of turbulence
,” Phys. Fluids
27
, 2229
(1984
);J.
Qian
, “Variational approach to the closure problem of turbulence theory
,” Phys. Fluids
26
, 2098
(1983
).14.
D. C. Leslie, Developments in the Theory of Turbulence (Clarendon, Oxford, 1983).
15.
J.
Qian
, “Inertial range and the finite Reynolds number effect of turbulence
,” Phys. Rev. E
55
, 337
(1997
).16.
R.
Benzi
, S.
Ciliberto
, R.
Tripiccione
, C.
Baudet
, F.
Massaioli
, and S.
Succi
, “Extended self-similarity in turbulent flows
,” Phys. Rev. E
48
, R29
(1993
);R.
Benzi
, S.
Ciliberto
, C.
Baudet
, and G. R.
Chavarria
, “On the scaling of three-dimensional homogeneous and isotropic turbulence
,” Physica D
80
, 385
(1995
).17.
J.
Qian
, “Scaling exponents of the second-order structure function of turbulence
,” J. Phys. A
31
, 3193
(1998
).18.
J.
Qian
, “Normal and anomalous scaling of turbulence
,” Phys. Rev. E
58
, 7325
(1998
);J.
Qian
, “Closure approach to high-order structure function of turbulence
,” Phys. Rev. Lett.
84
, 646
(2000
);J.
Qian
, “Quasi-closure and scaling of turbulence
,” Int. J. Mod. Phys. B
15
, 1085
(2001
).19.
J.
Qian
, “Slow decay of the finite Reynolds number effect of turbulence
,” Phys. Rev. E
60
, 3409
(1999
).20.
I.
Arad
, B.
Dhruva
, S.
Kurien
, V. S.
L’vov
, I.
Procaccia
, and K. R.
Sreenivasan
, “Extraction of anisotropic contributions in turbulent flows
,” Phys. Rev. Lett.
81
, 5330
(1998
).21.
S.
Kurien
, V. S.
L’vov
, I.
Procaccia
, and K. R.
Sreenivasan
, “Scaling structure of the velocity statistics in atmospheric boundary layers
,” Phys. Rev. E
61
, 407
(2000
).22.
J.
Qian
, “Scaling of structure functions in homogeneous shear-flow turbulence
,” Phys. Rev. E
63
, 036301
(2002
).23.
A. A.
Praskovsky
, “Experimental verification of the Kolmogorov refined similarity hypothesis
,” Phys. Fluids A
4
, 2589
(1992
).24.
J.
Qian
, “Correlation coefficients between the velocity difference and local average dissipation of turbulence
,” Phys. Rev. E
54
, 981
(1996
).
This content is only available via PDF.
© 2003 American Institute of Physics.
2003
American Institute of Physics
You do not currently have access to this content.
