Optical depth in particle-laden turbulent flows

- Turbulent particle clustering increases radiation transmission through clouds.
- The two-point correlation for particle concentration is derived from a radial distribution function.
- A general closure model for the turbulence-radiation interaction is derived.
- The model is validated against particle-resolved ray tracing results.

Turbulent clustering of particles causes an increase in the radiation transmission through gas-particle mixtures. Attempts to capture the ensemble-averaged transmission lead to a closure problem called the turbulence-radiation interaction. A simple closure model based on the particle radial distribution function is proposed to capture the effect of turbulent fluctuations in the concentration on radiation intensity. The model is validated against a set of particle-resolved ray tracing experiments through particle fields from direct numerical simulations of particle-laden turbulence. The form of the closure model is generalizable to arbitrary stochastic media with known two-point correlation functions.