Abstract-
The most casual observer notices that atmospheric clouds are turbulent, yet
we still struggle to understand the detailed role of turbulence in cloud
physics. For example, current understanding of fundamental processes in
clouds such as the collision and coalescence of droplets and the
propagation of electromagnetic radiation, is based on the assumption that
droplets are distributed in space in a perfectly random manner at small
(e.g., sub-meter) scales. In fact, droplets in a cloud often do not follow
what we might call the Poisson assumption, but instead are 'clustered' on
various scales. Correlations in droplet positions can be caused by
turbulent mixing of cloudy and clear air, by the inertial response of cloud
droplets to fluid accelerations, or even by gravitational sedimentation in
still air. To describe correlations at the small scales relevant to
droplet-droplet interactions we set aside the notion of a continuous scalar
variable, such as droplet number density, and instead adopt a language
capable of describing a discrete, countable, scalar variable. The degree
of spatial correlation is then quantified by the pair correlation function,
and its scale dependence varies with such variables as droplet size, energy
dissipation rate, and turbulence Reynolds number. Spatial correlations
measured in turbulent clouds are observed to be strongest at centimeter
scales and below and the pronounced clustering on these scales is
consistent with the inertial clustering hypothesis.
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