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Discontinuity, Nonlinearity, and Complexity 4(3) (2015) 313--321 | DOI:10.5890/DNC.2015.09.007

Boris Shmerlin$^{1}$, Maxim Kalashnik$^{1}$,$^{2}$, Mikhail Shmerlin$^{1}$

$^{1}$ Federal State Budgetary Institution “Research and Production Association “Typhoon”, 4 Pobedy street, 249038 Obninsk Kaluga region, Russia

$^{2}$ Obninsk Institute for Nuclear Power Engineering, branch of “MEPhI” National Research Nuclear University, 249040 Obninsk Kaluga region, Russia

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Abstract

The classical Rayleigh theory of convective instability of a viscous and heat conductive rotating atmospheric layer is generalized to the case of phase transitions of water vapor both for the precipitation convection (PC) and for the nonprecipitation (NPC) one. A principal difference is stated between moist convection and Rayleigh convection, on the one hand, and PC and NPC, on the other hand. In particular, the instability region on the plane of model parameters turned out to generally consist of two subregions, in one of which the localized axisymmetric disturbances with a tropical cyclone (hurricane) structure have the highest growth rate. In case of PC the ascending motions on the axis of symmetry correspond to such disturbances, in case of NPC a spontaneous growth of localized vortices both with ascending and descending motions on the axis is possible. Under other parameters values in case of PC spatially periodic cloud structures (convective rolls or closed cloud cells) have the highest growth rate and in case of NPC–mesoscale systems of convective rolls or mesoscale cloud clusters with annular cloud structures.

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