Convective instability of a water-vapor-saturated atmospheric layer. The formation of localized and periodic cloud struc
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TICAL, NONLINEAR, AND SOFT MATTER PHYSICS
Convective Instability of a WaterVaporSaturated Atmospheric Layer. The Formation of Localized and Periodic Cloud Structures B. Ya. Shmerlina,*, M. V. Kalashnika,b,c, and M. B. Shmerlina,d a
Scientific and Production Association “Typhoon,” Institute of Experimental Meteorology, Obninsk, Kaluga oblast, 249038 Russia bObukhov Institute of Atmospheric Physics, Russian Academy of Sciences, Moscow, 109017 Russia c Obninsk Institute for Nuclear Power Engineering, branch of “MEPhI” National Research Nuclear University, Obninsk, Kaluga oblast, 249040 Russia d Geophysical Service of the Russian Academy of Sciences, Obninsk, Kaluga oblast, 249035 Russia *email: [email protected] Received May 11, 2012
Abstract—The classical Rayleigh problem of convective instability is generalized to the case of water vapor condensation in the atmosphere. We present an analytical solution demonstrating a fundamental difference between moist convection and Rayleigh convection: the curve of the critical Rayleigh number versus the number characterizing the intensity of condensation heat release consists of two parts, with spatially localized neutral solutions corresponding to one of them. Spatially periodic neutral solutions correspond to the second part of the curve; these are characterized by a significant localization of the regions of ascending motions. The theory describes the nucleation and development of individual convective clouds and ordered cloud struc tures. DOI: 10.1134/S1063776112130158
1. INTRODUCTION The moist convection processes are most pro nounced above oceans. Satellite photographs reveal various ordered convective structures in the shape of periodic cloud banks or spatial convective cells. Fun damental inconsistencies of the parameters of cloud structures with predictions of the Rayleigh convective instability model have long been established. The ratio of the horizontal size of a convective cell to the vertical one in the Rayleigh model is of the order of unity, while for observed cloud structures it can reach 30 or more [1–3]. Another clear inconsistency is associated with the observed asymmetry in the distribution of ascending and descending motions—the area of the cloud cover or the area of the ascending motions can account for less than 10% of the entire area affected by ordered convection [2, 3]. Therefore, a generalized formulation of the classical Rayleigh problem, investi gation of the stability of the equilibrium state for a layer of moist saturated air, was considered in a num ber of papers. As a rule, a simplified approach based on the inclusion of a volume condensation heat source that is proportional to the vertical velocity on the ascending branch of the circulation and is absent (becomes zero) on the descending one in the thermal convection equations is used to study the moist con vection dynamics. This idea corresponds to the con densation of a water vapor excess with the release of latent heat and the precipitation of droplets in the
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