  The dynamics of heavy particles suspended in turbulent flows is of
fundamental importance for a wide range of questions in astrophysics,
atmospheric physics, oceanography, and technology. Laboratory experiments and
numerical simulations have demonstrated that heavy particles respond in
intricate ways to turbulent fluctuations of the carrying fluid: non-interacting
particles may cluster together and form spatial patterns even though the fluid
is incompressible, and the relative speeds of nearby particles can fluctuate
strongly. Both phenomena depend sensitively on the parameters of the system.
This parameter dependence is difficult to model from first principles since
turbulence plays an essential role. Laboratory experiments are also very
difficult, precisely since they must refer to a turbulent environment. But in
recent years it has become clear that important aspects of the dynamics of
heavy particles in turbulence can be understood in terms of statistical models
where the turbulent fluctuations are approximated by Gaussian random functions
with appropriate correlation functions. In this review we summarise how such
statistical-model calculations have led to a detailed understanding of the
factors that determine heavy-particle dynamics in turbulence. We concentrate on
spatial clustering of heavy particles in turbulence. This is an important
question because spatial clustering affects the collision rate between the
particles and thus the long-term fate of the system.
