Anisotropic clustering and particles velocity statistics in shear turbulence

Abstract

Dynamics of inertial particles is addressed in a homogeneous shear flow as the prototype of statistically steady anisotropic flows. In this simple flow, velocity fluctuations are strongly anisotropic at the largest scales where production of turbulent kinetic energy is active i.e. at scale separation $$ r > L_S \left( {L_S } \right) = \sqrt {\varepsilon /S^3 } $$ denote the shear scale) while re-isotropization is expected for smaller separations $$ r < L_S $$ [6]. Since anisotropy is strongly depleted through the inertial range, the advecting field anisotropy may be expected in-influential for the small scale features of particle dynamics. We find instead that the small scales of the particle distribution and particles velocity fluctuations are strongly affected by the geometry of turbulent fluctuations at large scales even in the range of scales where isotropization of velocity statistics occurs. Inertial particles differ from perfectly Lagrangian tracers due to inertia which prevents them from following the flow trajectories. The main effect consists of “preferential accumulation” that leads to small-scale clustering for locally homogeneous and isotropic flows [1] and to turbophoresis in wallbounded flows i.e. preferential spatial segregation at the boundary [3]. The statistically steady homogeneous shear flow retains most of the anisotropic dynamics of wall bounded flows still preserving, spatial homogeneity. This flow shares with the wall-layer streamwise vortices and turbulent kinetic energy production mechanisms. Velocity fluctuations are strongly anisotropic at the large scales driven by production while, for smaller separations, the classical energy transfer mechanisms become effective in inducing re-isotropization.