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Stability properties of and scaling laws for a dry radiative‐convective atmosphere
Author(s) -
Larson Vincent E.
Publication year - 2000
Publication title -
quarterly journal of the royal meteorological society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.744
H-Index - 143
eISSN - 1477-870X
pISSN - 0035-9009
DOI - 10.1002/qj.49712656208
Subject(s) - radiative transfer , convection , physics , mechanics , radiative flux , convective heat transfer , scaling , rayleigh number , nonlinear system , thermal diffusivity , amplitude , classical mechanics , thermodynamics , natural convection , mathematics , geometry , optics , quantum mechanics
Abstract This work is a theoretical and numerical study of the stability properties and scaling laws associated with an idealized radiative‐convective model. We find that the linear‐stability threshold in the model can be described by a radiative Rayleigh number, a parameter that incorporates radiative effects but otherwise resembles the classical Rayleigh number. The energy method is used to find a nonlinear‐stability threshold below which all perturbations, whether infinitesimal or finite‐amplitude, decay. The model behaviour when weakly nonlinear convection occurs is studied via the mean‐field equations. We find that changing the values of viscosity, thermal diffusivity, and radiative damping has only weak effects on the vertical convective heat flux, in contrast to the case for weakly nonlinear Rayleigh‐Bénard convection. Finally, we propose scaling laws for the vertical convective heat flux, vertical velocity, and temperature perturbations.