Coagulation dynamics under random field: turbulence effects on rain

TL;DR

This paper investigates how turbulence modeled as a random field influences rain droplet growth and formation, using particle systems and convergence analysis, complemented by numerical simulations to understand noise effects.

Contribution

It introduces a stochastic particle system approach to model turbulence effects on rain formation and proves convergence to a limiting equation under various random field settings.

Findings

Empirical density converges to the solution of a limiting equation.

Noise impacts the effectiveness of rain formation.

Numerical simulations illustrate turbulence effects on droplet aggregation.

Abstract

Turbulence in growth of rain droplets and rain formation is studied under an approximating particle system representing aggregation at the level of individuals, depending on their volume and distance in space, of the Smoluchowski Coagulation equation. A random field is introduced to model the air flow interaction with the particles and it is proved that the empirical density of the individual converges to solutions of limiting equation under different setting for the random field of interaction. A brief numerical study for the continuous density is proposed using the particles approach, to analyze how noise can arise in such system and the effectiveness on rain formation.