Asymptotics for moist deep convection I: refined scalings and self-sustaining updrafts

• Published in: Theoretical and computational fluid dynamics Vol. 32; no. 2; pp. 137 - 164
• Main Authors: Hittmeir, Sabine, Klein, Rupert
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2018; Springer; Springer Nature B.V
• Subjects: Analysis; Asymptotic properties; Atmospheric convection; Atmospheric models; Classical and Continuum Physics; Closures; Coding; Computational Science and Engineering; Convection; Diagnostic systems; Dynamic meteorology; Dynamics; Engineering; Engineering Fluid Dynamics; Forces (mechanics); Frameworks; Gases; Hamilton-Jacobi equations; Life cycle; Life cycle engineering; Life cycles; Mathematical models; Meteorology; Microphysics; Mixing ratio; Modelling; Multiscale analysis; Original Article; Potential energy; Scaling; Solutions; Storms; Towers; Tropical climate; Vertical forces; United States; Matched asymptotic expansions; Moist atmospheric flows; Multiscale asymptotics; Hot towers; Cumulonimbus clouds
• ISSN: 0935-4964; 1432-2250
• DOI: 10.1007/s00162-017-0443-z

Moist processes are among the most important drivers of atmospheric dynamics, and scale analysis and asymptotics are cornerstones of theoretical meteorology. Accounting for moist processes in systematic scale analyses therefore seems of considerable importance for the field. Klein and Majda (Theor Comput Fluid Dyn 20:525–551, 2006 ) proposed a scaling regime for the incorporation of moist bulk microphysics closures in multiscale asymptotic analyses of tropical deep convection. This regime is refined here to allow for mixtures of ideal gases and to establish consistency with a more general multiple scales modeling framework for atmospheric flows. Deep narrow updrafts, the so-called hot towers, constitute principal building blocks of larger scale storm systems. They are analyzed here in a sample application of the new scaling regime. A single quasi-one-dimensional upright columnar cloud is considered on the vertical advective (or tower life cycle) time scale. The refined asymptotic scaling regime is essential for this example as it reveals a new mechanism for the self-sustainance of such updrafts. Even for strongly positive convectively available potential energy, a vertical balance of buoyancy forces is found in the presence of precipitation. This balance induces a diagnostic equation for the vertical velocity, and it is responsible for the generation of self-sustained balanced updrafts. The time-dependent updraft structure is encoded in a Hamilton–Jacobi equation for the precipitation mixing ratio. Numerical solutions of this equation suggest that the self-sustained updrafts may strongly enhance hot tower life cycles.