Abstract
The linear hydrodynamic instability of the spatially periodic system of updrafts and downdrafts in a stably stratified atmosphere is studied. Such formulation of the problem is used to simulate the cloud systems observed in the atmosphere, when the zones of updrafts correspond to clouds and those of downdrafts correspond to intercloud intervals. A rather unexpected conclusion was made that the consideration of turbulent viscosity and thermal conductivity of the atmosphere as well as of radiative cooling leads to the instability at the Richardson numbers exceeding the critical value of 1/8 for the nondissipative case.
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References
V. P. Dymnikov, “On the Development of Baroclinic Instability in an Atmosphere with a Variable Static Stability Parameter,” Izv. Akad. Nauk, Fiz. Atmos. Okeana, No. 5, 14 (1978) [Atmos. Ocean Phys., No. 5, 1 (1978)].
V. P. Dymnikov and A. N. Filatov, Stability of Large–scale Atmospheric Processes (Gidrometeoizdat, Leningrad, 1990) [in Russian].
M. V. Kurgansky, “Instability of Internal Gravity Waves Propagating at Small Angles to the Vertical,” Izv. Akad. Nauk, Fiz. Atmos. Okeana, No. 10, 16 (1980) [Atmos. Ocean Phys., No. 10, 16 (1980)].
L. D. Meshalkin and Ya. G. Sinai, “Investigation of the Stability of a Stationary Solution of a System of Equations for the Plane Movement of an Incompressible Viscous Liquid,” Prikladnaya Matematika i Mekhanika, No. 6, 25 (1961) [J. Appl. Math. Mech., No. 6, 25 (1961)].
N. Balmforth and Y.–N. Young, “Stratified Kolmogorov Flow,” J. Fluid Mech., 450 (2002).
M. Gryschka, J. Fricke, and S. Raasch, “On the Impact of Forced Roll Convection on Vertical Turbulent Transport in Cold Air Outbreaks,” J. Geophys. Res. Atmos., 119 (2014).
M. Kalashnik and M. Kurgansky, “Nonlinear Dynamics of Long–wave Perturbations ofthe Kolmogorov Flow,” Ocean Dynamics, 68 (2018).
A. Libin, G. Sivashinsky, and E. Levich, “Long–wave Instability of Periodic Flows at Large Reynolds Numbers,” Phys. Fluids, 30 (1987).
M. E. McIntyre, “Diffusive Destabilization of the Baroclinic Circular Vortex,” Geophys. Fluid Dyn, 1 (1970).
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Original Russian Text © M.V. Kalashnik, M.V. Kurgansky, 2018, published in Meteorologiya i Gidrologiya, 2018, No. 11, pp. 31–40.
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Kalashnik, M.V., Kurgansky, M.V. Hydrodynamic Instability of the Periodic System of Updrafts and Downdrafts in the Atmosphere. Russ. Meteorol. Hydrol. 43, 729–736 (2018). https://doi.org/10.3103/S1068373918110031
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DOI: https://doi.org/10.3103/S1068373918110031