The statistics of a turbulent passive scalar (temperature) and
their Reynolds
number dependence are studied in decaying grid turbulence for the Taylor-microscale
Reynolds number, Rλ, varying from 30 to 731
(21[les ]Peλ[les ]512). A principal objective
is, using a single (and simple) flow, to bridge the gap between the existing
passive
grid-generated low-Péclet-number laboratory experiments and those
done
at high Péclet number in the atmosphere and oceans. The turbulence
is generated by means of an active grid and the passive temperature
fluctuations are generated by a mean transverse
temperature gradient, formed at the entrance to the wind tunnel plenum
chamber by
an array of differentially heated elements. A well-defined inertial–convective
scaling
range for the scalar with a slope, nθ,
close to the Obukhov–Corrsin value of 5/3, is
observed for all Reynolds numbers. This is in sharp contrast with the velocity
field,
in which a 5/3 slope is only approached at high
Rλ. The Obukhov–Corrsin constant,
Cθ, is estimated to be 0.45–0.55.
Unlike the velocity spectrum, a bump occurs in the
spectrum of the scalar at the dissipation scales, with increasing prominence
as the
Reynolds number is increased. A scaling range for the heat flux cospectrum
was also
observed, but with a slope around 2, less than the 7/3 expected from
scaling theory.
Transverse structure functions of temperature exist at the third and fifth
orders, and,
as for even-order structure functions, the width of their inertial subranges
dilates
with Reynolds number in a systematic way. As previously shown for shear
flows,
the existence of these odd-order structure functions is a violation of
local isotropy
for the scalar differences, as is the existence of non-zero values of the
transverse
temperature derivative skewness (of order unity) and hyperskewness (of
order 100).
The ratio of the temperature derivative standard deviation along and normal
to the
gradient is 1.2±0.1, and is independent of Reynolds number. The
refined similarity
hypothesis for the passive scalar was found to hold for all
Rλ, which was not the case
for the velocity field. The intermittency exponent for the scalar,
μθ, was found to be
0.25±0.05 with a possible weak Rλ
dependence, unlike the velocity field, where μ was
a strong function of Reynolds number. New, higher-Reynolds-number results
for the
velocity field, which smoothly follow the trends of Mydlarski & Warhaft
(1996), are
also presented.