Global well-posedness for the thermodynamically refined passively transported nonlinear moisture dynamics with phase changes

TL;DR

This paper proves the global existence and uniqueness of solutions for a refined model of moisture dynamics with phase changes in warm clouds, incorporating detailed thermodynamic effects.

Contribution

It introduces a more complex thermodynamic model for moisture dynamics, accounting for different gas constants and heat capacities, and establishes its well-posedness.

Findings

Global solvability of the refined moisture model

Enhanced coupling between moisture and thermodynamics

Necessary a priori estimates for solution existence

Abstract

In this work we study the global solvability of moisture dynamics with phase changes for warm clouds. We thereby in comparison to previous studies [Hittmeir-Klein-Li-Titi (2017)] take into account the different gas constants for dry air and water vapor as well as the different heat capacities for dry air, water vapor and liquid water, which leads to a much stronger coupling of the moisture balances and the thermodynamic equation. This refined thermodynamic setting has been demonstrated to be essential e.g. in the case of deep convective cloud columns in [Hittmeir-Klein (2017)]. The more complicated structure requires careful derivations of sufficient a priori estimates for proving global existence and uniqueness of solutions.