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Figure 7.2 A time series of temperature measured in a heated jet showing
“ramp-cliff” structure. From Warhaft ( 2000 ). Reprinted, with permission,
from Annual Review of Fluid Mechanics , 32 , ©2000 by Annual Reviews,
www.annualreviews.org .
isotropy at very large R t was also plausible. But as measurements revealed instan-
taneous details of scalar fine structure - e.g., Figure 7.2 - it became clear that the
largest and smallest eddies in a turbulent flow can directly and persistently interact.
Kang and Meneveau ( 2001 ), for example, have found that in moderate Reynolds
number ( R λ =
350) laboratory turbulence local anisotropy is more pronounced in
the scalar field than in the velocity field.
Given the inherent anisotropy of the energy-containing range, Kolmogorov's
( 1941 ) local isotropy is an asymptotic, large- R t hypothesis. At the modest R t val-
ues typical of laboratory turbulence some local anisotropy is to be expected, and
the skewness of a temperature derivative, say, is precisely zero there only as a con-
sequence of flow symmetry. Consider, for example, the turbulent wake behind a
long cylinder in crossflow, with x the streamwise direction and y along the cylinder
axis. Here, by symmetry, statistics are invariant to a reversal of the y -direction, and
so the skewness of θ ,y is zero. Local isotropy would imply that the skewness of θ ,x
approaches zero at large R t .But Sreenivasan ( 1991 ) pointed out that it shows little
evidence of this asymptotic behavior, and he concluded:
Experiments suggest that local isotropy is not a natural concept for scalars in shear flows,
except perhaps at such extreme Reynolds numbers that are of no practical relevance on Earth.
Warhaf t ( 2000 ) has written:
We surmise that had we not been imbued with the Kolmogorov phenomenology, …a fun-
damentally anisotropic scalar field would seem natural. We would expect that, as the large
eddies act on the scalar gradient, large discontinuities might occur. It is the very strong
attraction to universality that has diverted our attention.
We'll consider local isotropy in more detail in Chapter 14 .
 
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