Shock trapping and inertial escape: Dust-particle clustering in compressible turbulence

Abstract

We study the dynamics and clustering of dust particles with inertia in shock-dominated compressible turbulence using the two-dimensional, stochastically forced Burgers equation. At small Stokes numbers, shock trapping leads to extreme density inhomogeneities and nearly singular aggregation, with correlation dimensions approaching zero. With increasing inertia, particles undergo inertial escape and intermittently cross shock fronts, producing a sharp crossover from shock-dominated trapping to quasi-ballistic dynamics. This crossover is accompanied by a pronounced reduction in density fluctuations, a continuous increase of the correlation dimension from zero to the embedding dimension, and a power-law dependence of density fluctuations on the Stokes number over an extended intermediate regime. In this regime, particle distributions show scale-free coarse-grained density statistics arising from repeated trap--escape dynamics. This behaviour is qualitatively distinct from inertial-particle clustering in incompressible turbulence and is directly relevant to dust concentration in shock-rich regions of protoplanetary discs and other compressible astrophysical environments.