The Physical Mechanism of CISK and the Free-Ride Balance

Abstract

The properties of the ?free-ride? assumption of balance between diabatic heating and adiabatic cooling are investigated by incorporating it into the classical two-level CISK (Conditional Instability of the Second Kind) model of Charney and Eliassen. The free-ride model is found to give a CISK-type instability when the heating amplitude exceeds the modified static stability (s?a?). The free-ride solution is very similar in structure to the CISK solution, except that the free-ride growth rate is independent of scale. Inspection of the classical CISK model reveals that its growth rate is also independent of scale over the range of scales for which the instability is efficient, and over this range of scales the free-ride and the classical models are essentially identical. This leads to a new physical interpretation of CISK. Given that the cumulonimbus heating rate is proportional (through the Ekman pumping effect) to the low-level vorticity, the CISK mechanism is interpreted in terms of a balance and a feedback. The balance is the free-ride balance between the (Ekman) heating and the adiabatic cooling by the divergent circulation. The feedback is through increase of the vorticity by the inward advection or angular momentum by the divergent circulation. This interpretation gives insight into the nature of the CISK mechanism. It explains why the characteristic CISK time scale is half the Ekman spin-down time, and why the space scale is an order of magnitude below the deformation radius. It also reveals that the CISK feedback is through the spinup brought about by the divergent circulation above the boundary layer.