Hydrodynamic Instability of the Periodic System of Updrafts and Downdrafts in the Atmosphere

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.