A correlated stochastic model for the large-scale advection, condensation and diffusion of water vapour

Abstract

The statistically steady distribution of water vapour and its characteristics are studied in the framework of the Ornstein–Uhlenbeck (OU) turbulent dispersion model. Particles are advected by a stochastic velocity field with a finite time correlation, and condense as soon as their moisture content exceeds a local saturation value. We discretize the OU model to a finite number of velocity values, and find simple analytical solutions for the bimodal distribution of water vapour and the non‐diffusive moisture flux, which perfectly agree with the corresponding Monte‐Carlo simulations. Furthermore, we show that these simple models produce results that approximate well the OU Monte‐Carlo simulations, suggesting that they could be used as general tools to understand correlated stochastic processes that involve condensation.