Wave-CISK in the Tropics

CISK (Conditional Instability of the Second Kind) is examined for internal waves where low-level convergence is due to the inviscid wave fields rather than to Ekman pumping. It is found that CISK-induced waves must give rise to mean cumulus activity (since there are no negative clouds), and it is suggested that this mean activity plays an important role in the finite-amplitude equilibration of the system. The most unstable CISK waves will be associated with very short vertical wavelengths O(3 km) in order to maximize (in some crude sense) subcloud convergence. Thus, the vertical scale is largely determined by the height of cloud base. The vertical scale, in turn, determines the dispersive relations between horizontal and temporal scales. It is found that there exists a wave-CISK mode which is independent of longitude, and hence independent of the mean zonal flow. Because of this independence, the period of this oscillation should form a prominent line in tropical spectra. This period turns out to be about 4.8 days which is indeed a prominent feature of tropical spectra. It is shown, due to longitudinal inhomogeneities in the tropics (such as land-sea), that the above oscillation must be accompanied by traveling disturbances whose period with respect to the ground will also be 4.8 days and whose longitudinal scales will typically be from 1000–3000 km depending on the mean zonal flow. It is further shown that the existence of the above oscillatory system has two additional implications: The above system is, itself, unstable with respect to gravity waves with horizontal scales on the order of 100–200 km. Such waves may be associated with cloud clusters. The above system leads to maximum low-level convergence (and hence, a tendency toward mean cumulus activity) in regions centered about ±6°–7° latitude, thus providing a possible explanation for the position of the ITCZ.