Systematic multiscale models for deep convection on mesoscales

Rupert Klein, Andrew J. Majda

Research output: Contribution to journalArticle

Abstract

This paper builds on recent developments of a unified asymptotic approach to meteorological modeling [ZAMM, 80: 765-777, 2000, SIAM Proc. App. Math. 116, 227-289, 2004], which was used successfully in the development of Systematic multiscale models for the tropics in Majda and Klein [J. Atmosph. Sci. 60: 393-408, 2003] and Majda and Biello [PNAS, 101: 4736-4741, 2004]. Biello and Majda [J. Atmosph. Sci. 62: 1694-1720, 2005]. Here we account for typical bulk microphysics parameterizations of moist processes within this framework. The key steps are careful nondimensionalization of the bulk microphysics equations and the choice of appropriate distinguished limits for the various nondimensional small parameters that appear. We are then in a position to study scale interactions in the atmosphere involving moist physics. We demonstrate this by developing two systematic multiscale models that are motivated by our interest in mesoscale organized convection. The emphasis here is on multiple length scales but common time scales. The first of these models describes the short-time evolution of slender, deep convective hot towers with horizontal scale ∼1 km interacting with the linearized momentum balance on length and time scales of (10 km/3 min). We expect this model to describe how convective inhibition may be overcome near the surface, how the onset of deep convection triggers convective-scale gravity waves, and that it will also yield new insight into how such local convective events may conspire to create larger-scale strong storms. The second model addresses the next larger range of length and time scales (10 km, 100 km, and 20 min) and exhibits mathematical features that are strongly reminiscent of mesoscale organized convection. In both cases, the asymptotic analysis reveals how the stiffness of condensation/evaporation processes induces highly nonlinear dynamics. Besides providing new theoretical insights, the derived models may also serve as a theoretical devices for analyzing and interpreting the results of complex moist process model simulations, and they may stimulate the development of new, theoretically grounded sub-grid-scale parameterizations.

Original languageEnglish (US)
Pages (from-to)525-551
Number of pages27
JournalTheoretical and Computational Fluid Dynamics
Volume20
Issue number5-6
DOIs
StatePublished - Nov 2006

Fingerprint

multiscale models
Multiscale Model
Convection
convection
Length Scale
Time Scales
Parameterization
Gravity Waves
timescale
Multiple Scales
Evaporation
Condensation
Trigger
Asymptotic Analysis
Small Parameter
Model
parameterization
Process Model
Nonlinear Dynamics
Atmosphere

Keywords

  • Moist processes
  • Multiple-scale asymptotics

ASJC Scopus subject areas

  • Fluid Flow and Transfer Processes
  • Oceanography
  • Computational Mechanics
  • Mechanics of Materials
  • Applied Mathematics
  • Physics and Astronomy(all)
  • Physics and Astronomy (miscellaneous)
  • Condensed Matter Physics

Cite this

Systematic multiscale models for deep convection on mesoscales. / Klein, Rupert; Majda, Andrew J.

In: Theoretical and Computational Fluid Dynamics, Vol. 20, No. 5-6, 11.2006, p. 525-551.

Research output: Contribution to journalArticle

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