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.