Repository: Freie Universit├Ąt Berlin, Math Department

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

Hittmeir, S. and Klein, R. (2018) Asymptotics for moist deep convection I: Refined scalings and self-sustaining updrafts. Theoretical and Computational Fluid Dynamics, 32 (2). pp. 137-164. ISSN 0935-4964 (Print) 1432-2250 (Online)


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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 & Majda (TCFD, vol. 20, 525--552, (2006)) proposed a scaling regime for the incorporation of moist bulk microphysics closures in multi-scale 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 modelling framework for atmospheric flows. Deep narrow updrafts, so-called "hot towers", constitute principal building blocks of larger scale storm systems. They are analysed here in a sample application of the new scaling regime. A single quasi-onedimensional 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 (CAPE), 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.

Item Type:Article
Additional Information:04/2017 SFB 1114 Preprint
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics > Geophysical Fluid Dynamics Group
ID Code:2070
Deposited By: Silvia Hoemke
Deposited On:19 Apr 2017 14:44
Last Modified:19 Mar 2019 13:09

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