Spectral characterisation of inertial particle clustering in turbulence
  Clustering of inertial particles is important for many types of astrophysical
and geophysical turbulence, but it has been studied predominately for
incompressible flows. Here we study compressible flows and compare clustering
in both compressively (irrotationally) and vortically (solenoidally) forced
turbulence. Vortically and compressively forced flows are driven stochastically
either by solenoidal waves or by circular expansion waves, respectively. For
compressively forced flows, the power spectrum of the density of inertial
particles is a useful tool for displaying particle clustering relative to the
fluid density enhancement. Power spectra are shown to be particularly sensitive
for studying large-scale particle clustering, while conventional tools such as
radial distribution functions are more suitable for studying small-scale
clustering. Our primary finding is that particle clustering through shock
interaction is particularly prominent in turbulence driven by spherical
expansion waves. It manifests itself through a double-peaked distribution of
spectral power as a function of Stokes number. The two peaks are associated
with two distinct clustering mechanisms; shock interaction for smaller Stokes
numbers and the centrifugal sling effect for larger values. The clustering of
inertial particles is associated with the formation of caustics. Such caustics
can only be captured in the Lagrangian description, which allows us to assess
the relative importance of caustics in vortically and compressively forced
turbulence. We show that the statistical noise resulting from the limited
number of particles in the Lagrangian description can be removed from the
particle power spectra, allowing us a more detailed comparison of the residual
spectra. We focus on the Epstein drag law relevant for rarefied gases, but show
that our findings apply also to the usual Stokes drag.
