Fractal distribution of water droplets in warm clouds
We consider motion of water droplets in clouds driven by gravity and turbulent drag of the air. We demonstrate that this motion can be described with the help of smooth spatial flow of particles. In contrast with the flow of the air, that of the droplets is compressible. We demonstrate using smallness of compressibility that droplets distribute over multifractal set. The pair-correlations obey power-law whose exponent is determined by the energy spectrum of the flow. We confirm the predictions with direct numerical simulations of the motion of droplets in Navier-Stokes turbulence.