Abstract
Solutions to the wave-CISK (conditional instability of the second kind with cumulus heating being induced by low-level internal wave convergence) system are obtained to study the vertical structure of orginally unstable waves. A diabatic heating profile is specified that resembles those observed and those theoretically derived from simple pararmeterization schemes. Upper and lower bounds for the vertical wavelength of the unstable waves under normal beating conditions are established through analysis of the frequency (stability) equation. The lower bound excludes the possibility of excitation or maintenance of short vertical wavelengths (relative to the vertical scale of heating) by wave-CISK. The calculated growth rates indicate that this result is basically insensitive to the vertical heating profile. The vertical structure of the most unstable waves is also computed and the possible roles played by CISK in large-scale tropical waves are discussed in light of these results.
