A Generalization of the CISK Theory

Abstract

The CISK theory is generalized by incorporating an explicit solution of the time-dependent boundary layer equations for the case of exponential growth and allowing the interior flow to be unbalanced. Two separate modes of solution are found, which are termed CISK of Types A and B. CISK of Type A, a generalization of the well-known CISK solution, has the following characteristics: the instability is essentially dependent on rotation, friction, and the latent energy of moisture converged at levels below cloud base; the low-level convergence is comprised of frictional and allobaric components which act in the same direction, their relative magnitudes depending on the ratio of the growth rate to the Coriolis parameter; and the growth rate increases with latitude and is bounded above by f/3. CISK of Type B, a new solution, has the following characteristics: the instability depends on friction but can exist without rotation; the energy is derived from moisture converged at levels above cloud base; the low-level convergence is opposed by friction and exists through the predominance of the allobaric effect; and the growth rate is bounded below by 1.8f and attains its maximum value on the equator. The mean thermodynamic parameters of the tropical atmosphere favor Type A CISK. However, the range of parameters required for the existence of Type B CISK would seem to be attainable. This may help to explain why the ITCZ cloud bands, though normally found away from the equator, are sometimes, observed on the equator.