Clustering and energy spectra in two-dimensional dusty gas turbulence

Studying turbulence in a fluid with background damping

In this experimental paper, we demonstrate that turbulence can develop in a fluid system with background damping. For that purpose, we analyze dust acoustic waves, self-excited in a fluid complex plasma where the motion of individual microparticles was recorded with a high-speed video camera. We use the Wiener-Khinchin theorem to calculate the kinetic spectrum during different phases of the highly nonlinear periodic wave motion and show that a turbulent cascade develops at the phases of highest particle compression. We demonstrate that the energy cascade occurs despite the presence of a damping force due to the background neutral gas.

Rate of formation of caustics in heavy particles advected by turbulence

The rate of collision and the relative velocities of the colliding particles in turbulent flows are a crucial part of several natural phenomena, e.g. rain formation in warm clouds and planetesimal formation in protoplanetary discs. The particles are often modelled as passive, but heavy and inertial. Within this model, large relative velocities emerge due to formation of singularities (caustics) of the gradient matrix of the velocities of the particles. Using extensive direct numerical simulations of heavy particles in both two (direct and inverse cascade) and three-dimensional turbulent flows, we calculate the rate of formation of caustics, [Formula: see text] as a function of the Stokes number ([Formula: see text]). The best approximation to our data is [Formula: see text], in the limit [Formula: see text] where [Formula: see text] is a non-universal constant. This article is part of the theme issue 'Scaling the turbulence edifice (part 2)'.