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National Advisory Committee for Aeronautics, Report - Diffusion of Heat From a Line Source in Isotropic Turbulence

An experimental and analytical study has been made of some
features of the turbulent heat difl'usion behind a line heated wire
stretched perpendicular to a flowing isotropic turbulence. The
mean temperature distributions have been measured with sys-
tematic variations in wind speed, size of turbulence—producing
grid, and downstream location of heat source. The nature of
the temperature fluctuation field has been studied.

A comparison of Lagrangian and Eiderian analyses for dif-
fusion in a nondecaying turbulence yields an expression for
turbulent-heat—transfer coefiicient in teams of turbulence velocity
and a Lagrangian “scale.”

The ratio of Euler-ion to Lagrangian microscale has been de-
termined theoretically by generalization of a result of Heisenberg
and, with arbitrary constants taken from independent sources,
shows rough agreement with experimental results.

A convenient form has been deduced for the criterion of inter-
changeability of instantaneous space and time derivatives in a
flowing turbulence.

One of the most striking aspects of turbulent motion in
fluids is its dispersive property. This “convective diflusion,”
illustrated by the general statistical tendency of (noncon-
tiguous) fluid elements to get farther apart with increasing
time, was probably first observed long before the era of
, analytical fluid mechanics. An analytical start on this
problem was not made, however, until the now-classic work
by Taylor in 1921 on diffusion by continuous movements
(reference 1). Not only did this paper lay a groundwork for
the study of turbulent diffusion but it also represented a
forward step in the ideas essential to development of a gen—
eral statistical theory of turbulence, a field which had scarcely
progressed since Reynolds’ original formulation of the equa—
tions of motion for a flow in which mean and fluctuating
parts could be distinguished.