(228b) Clustering of Heavy Particles in Turbulence – Dimensional Analysis and Scaling Laws in the Inertial Range

High-resolution direct numerical simulations of small particles embedded in a turbulent flow field show that the particles accumulate in regions of high strain and low vorticity. While clustering is more dramatic at small scales, it is also observed throughout the inertial range of turbulence. We present a statistical theory for the scaling law of the two-particle distribution function in the inertial range. The scaling is developed with the aid of dimensional analysis similar to that taught by Professor Churchill in his graduate course on heat transfer, which laid out the simple, yet profound guidance obtained from the constraints imposed by the units of the relevant variables. Even in this completely different application, those insights I learned 30 years ago played a vital role in helping us understand and model clustering in the inertial range.