The non-existence of wave-CISK in the tropical regions

The proof of non-existence of wave-CISK in the tropics will be presented For Kelvin waves, Rossby waves, and mixed Rossby-Gravity waves. Ther governing equations are the primitive equations but excpanded on the equatorial beta plane.

The proof of the Kelvin waves hasnpreviously presented in printed form.Because the Kelvin waves are non-dispersive waves, The merthod of characterristics can be used. However, the same methodf can not be applied to Rossby and mixed Rossby-Gravity waves, because these waves are dispersive waves. For the instability of these waves, one need to examine the dispersion relations of the waves. For the stability of the waves one needs only to show tyhat the wave frequency or the phase speed is always a real number.

This, if it is true, has far reaching consequences. All theories which depends onwave-CISKis no longer valid. The proof, of course, will depends on the cumulus parameterization scheme used. The proof with other schemes will be commented on.