PQG-DL-Ekman: a triple-deck boundary layer theory for large-scale atmospheric flow with moist process closures

Abstract

Reduced mathematical models for atmospheric dynamics at various scales have a long and rich history. However, versions of such models that explicitly incorporate moisture and phase changes have been developed only fairly recently. This work merges one of said modeling innovations, namely Smith and Stechmann's \emph{precipitating quasigeostrophic} (PQG) model family, with a triple-deck boundary layer theory due to Klein et al.~that extends the classical QG-Ekman theory by an intermediate \emph{diabatic layer} (DL). A detailed analysis of the Clausius-Clapeyron relation and Kessler-type bulk microphysics closures is included in the systematic derivation of the resulting PQG-DL-Ekman theory. Furthermore, to illustrate some of the model's properties, explicit axisymmetric solutions of the precipitating diabatic layer equations are derived and combined with numerical sample solutions for the bulk flow.