A new timescale for turbulence modulation by particles

A new timescale for turbulence modulation by particles is introduced. This timescale is inversely proportional to the number density and the radius of particles and can be regarded as a counterpart of the phase relaxation time, an important timescale in cloud physics, which characterizes the interaction between turbulence and cloud droplets by condensation-evaporation. Scaling analysis and direct numerical simulations of dilute inertial particles in homogeneous isotropic turbulence suggest that turbulence modulation by particles can be expressed as a function of the mass-loading parameter and the Damkohler number, which is defined as the ratio of the turbulence large-eddy turnover time to the new timescale.