The Characteristic Feature of Thermal Convection in the Atmosphere (I)

Case of dry convection

Abstract

Introducing the characteristic scales of thermal convection, 1/k and 1/m, in the horizontal and vertical directions respectively, the time evolution of total kinetic energy of the system and the life time of thermal convection are qualitatively discussed in a dry air case. According
to the linear theory of thermal convection, the disturbance in the unstable atmosphere develops exponentially with time. In this paper, it is qualitatively shown that the exponential amplification of amplitude of unstable disturbance with time is suppressed by the modification of mean static stability due to the upward eddy transport of entropy. In this process, the second-order effect on the mean static stability due to the presence of unstable disturbance is emphasized. The characteristic life time of thermal convection is roughly estimated and it is proportional to (1+m2/k²)^1/2.
In order to examine the qualitative discussion mentioned above, the numerical experiment of thermal convection in a dry air case is performed. The results show in good agreement with those obtained by the qualitative discussion.