Coagulation of inertial particles in supersonic turbulence
  Coagulation driven by supersonic turbulence is primarily an astrophysical
problem because coagulation processes on Earth are normally associated with
incompressible fluid flows at low Mach numbers, while dust aggregation in the
interstellar medium (ISM) for instance is an example of the opposite regime. We
study coagulation of inertial particles in compressible turbulence using
high-resolution direct and shock-capturing numerical simulations with a wide
range of Mach numbers from nearly incompressible to moderately supersonic. The
particle dynamics is simulated by representative particles and the effects on
the size distribution and coagulation rate due to increasing Mach number is
explored. We show that the time evolution of particle size distribution mainly
depends on the compressibility (Mach number). We find that the average
coagulation kernel $\langle C_{ij}\rangle$ scales linearly with the average
Mach number $\mathcal{M}_{\rm rms}$ multiplied by the combined size of the
colliding particles, that is, $\langle C_{ij}\rangle \sim \langle (a_i +
a_j)^3\rangle\, \mathcal{M}_{\rm rms}\tau_\eta^{-1}$, which is qualitatively
consistent with expectations from analytical estimates. A quantitative
correction $\langle C_{ij}\rangle \sim \langle(a_i + a_j)^3\rangle(v_{\rm
p,rms}/c_{\rm s})\tau_\eta^{-1}$ is proposed and can serve as a benchmark for
future studies. We argue that the coagulation rate $\langle R_c\rangle$ is also
enhanced by compressibility-induced compaction of particles.
