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Minimal models for precipitating turbulent convection

Published online by Cambridge University Press:  01 February 2013

Gerardo Hernandez-Duenas
Department of Mathematics, University of Wisconsin–Madison, Madison, WI 53706, USA
Andrew J. Majda
Department of Mathematics and Center for Atmosphere and Ocean Science, Courant Institute of Mathematical Sciences, New York University, New York, NY 10012-1110, USA
Leslie M. Smith
Department of Mathematics, University of Wisconsin–Madison, Madison, WI 53706, USA Department of Engineering Physics, University of Wisconsin–Madison, Madison, WI 53706, USA
Samuel N. Stechmann*
Department of Mathematics, University of Wisconsin–Madison, Madison, WI 53706, USA Department of Atmospheric and Oceanic Sciences, University of Wisconsin–Madison, Madison, WI 53706, USA
Email address for correspondence:


Simulations of precipitating convection would typically use a non-Boussinesq dynamical core such as the anelastic equations, and would incorporate water substance in all of its phases: vapour, liquid and ice. Furthermore, the liquid water phase would be separated into cloud water (small droplets suspended in air) and rain water (larger droplets that fall). Depending on environmental conditions, the moist convection may organize itself on multiple length and time scales. Here we investigate the question, what is the minimal representation of water substance and dynamics that still reproduces the basic regimes of turbulent convective organization? The simplified models investigated here use a Boussinesq atmosphere with bulk cloud physics involving equations for water vapour and rain water only. As a first test of the minimal models, we investigate organization or lack thereof on relatively small length scales of approximately 100 km and time scales of a few days. It is demonstrated that the minimal models produce either unorganized (‘scattered’) or organized convection in appropriate environmental conditions, depending on the environmental wind shear. For the case of organized convection, the models qualitatively capture features of propagating squall lines that are observed in nature and in more comprehensive cloud resolving models, such as tilted rain water profiles, low-altitude cold pools and propagation speed corresponding to the maximum of the horizontally averaged, horizontal velocity.

©2013 Cambridge University Press

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