A recursive relation for the unit isotropic tensor of an arbitrary even order is derived from a rotational Brownian motion of the unit vector. An expression for the eighth‐order velocity gradient correlation function is derived from the eighth‐order isotropic tensors, after preserving the solenoidal property of the velocity field. This correlation function is compared with measurements in a turbulent wake.
REFERENCES
1.
H. Jeffreys, Cartesian Tensors (Cambridge University Press, Cambridge, 1931).
2.
H. Weyl, The Classical Group (Princeton University Press, Princeton, NJ, 1939).
3.
E. A.
Kearsley
and J. T.
Fong
, “Linearly independent sets of isotropic Cartesian tensors of ranks up to eight
,” J. Res. Nat. Bur. Stand. B. Math. Sci.
79
, 49
(1975
).4.
H. P.
Robertson
, “The invariant theory of isotropic turbulence
,” Proc. Cambridge Philos. Soc.
36
, 209
(1940
).5.
F. H.
Champagne
, “The fine-scale structure of the turbulent velocity field
,” J. Fluid Mech.
86
, 67
(1978
).6.
R. B. Bird, C. F. Curtiss, R. C. Armstrong, and O. Hassager, Dynamics of Polymeric Liquids, 2nd ed. (Wiley, New York, 1987).
7.
J. C. Wyngaard (private communication).
8.
C. H.
Gibson
, C. A.
Friehe
, and S. O.
McConnell
, “Structure of sheared turbulent fields
,” Phys. Fluids
20
, S156
(1977
).9.
E. D.
Siggia
, “Invariants for the one-point vorticity and strain rate correlation functions
,” Phys. Fluids
24
, 1934
(1981
).10.
L. W. B.
Browne
, R. A.
Antonia
, and D. A.
Shah
, “Turbulent energy dissipation in a wake
,” J. Fluid Mech.
179
, 307
(1987
).11.
J. Mi and R. A. Antonia, “Vorticity characteristics in the intermediate wake of a cylinder,” submitted to Exp. Fluids.
12.
R. A.
Antonia
, F.
Anselmet
, and A. J.
Chambers
, “Assessment of local isotropy using measurements in a turbulent plane jet
,” J. Fluid Mech.
163
, 365
(1986
).13.
R. A.
Antonia
and J.
Kim
, “A numerical study of local isotropy of turbulence
,” Phys. Fluids
6
, 834
(1994
).
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© 1994 American Institute of Physics.
1994
American Institute of Physics
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