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Ann. Geophys., 21, 2201-2218, 2003
www.ann-geophys.net/21/2201/2003/
© European Geosciences Union 2003
A theoretical model for double diffusive phenomena in cloudy convection
P.-A. Bois1 and A. Kubicki1,2
1Laboratoire de Mécanique de Lille, UMR CNRS 8107, U.F.R de Mathématiques, Bât. M3, U.S.T.L., F-59655 Villeneuve d’Ascq, France
2now at: The Service d’Aéronomie, UMR CNRS 7620, Tour 25, 4 Place Jussieu , F-75252 Paris Cedex, France
Abstract. Using classical
rheological principles, a model is proposed to depict the molecular diffusion
in a moist-saturated dissipative atmosphere: due to the saturation condition
existing between water vapor and liquid water in the medium, the equations are
those of a double diffusive phenomenon with Dufour effect. The double
diffusivity is important because of the huge diffusivity difference between the
liquid phase and the gaseous phase. Reduced equations are constructed and are
then applied to describe the linear free convection of a thin cloudy layer
bounded by two free surfaces. The problem is solved with respect to two
destabilizing parameters, a Rayleigh number Ra and a moist
Rayleigh number Rh . Two instabilities may occur: (i)
oscillatory modes, which exist for sufficiently large values of the Rayleigh
number: these modes generalize the static instability of the medium; (ii)
stationary modes, which mainly occur when the moist Rayleigh number is
negative. These modes are due to the molecular diffusion, and exist even when
the medium is statically stable: the corresponding motions describe, in the
moist-saturated air, configurations such as "fleecy clouds". Growth
rates are determined at the instability threshold for the two modes of
instability occurring in the process. The case of vanishing moisture
concentration is considered: the oscillatory unstable case appears as a
singular perturbation (due to the moisture) of the stationary unstable state of
the Rayleigh-Bénard convection in pure fluid, and, more generally, as the
dynamical perturbation of the static instability. The convective behaviour of a
cloud in the air at rest is then examined: the instability of the cloud is
mainly due to moisture, while the instability of the surrounding air is mainly
due to heating.
Key words. Atmospheric composition
and structure (cloud physics and chemistry) – Meteorology and atmospheric
dynamics (convective processes, mesoscale meteorology)
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