Turbulent clustering of stagnation points and inertial particles

Abstract

In high-Reynolds-number two-dimensional turbulence with a −5/3 power-law energy spectrum, the clustering of inertial particles reflects the clustering of acceleration stagnation points for all particle relaxation times smaller than the integral time scale $T$ of the turbulence. Acceleration stagnation points and small inertial particles on these points are swept together by large-scale motions. In synthetic turbulence where there is no sweeping and acceleration stagnation points do not cluster, inertial particles do nevertheless cluster as a result of the repelling action of persistent velocity stagnation-point clusters. This repelling action has a negligible effect on the clustering of inertial particles in the presence of acceleration stagnation points clustering.