Abstract
The dependence of Kelvin and Rossby wave CISK (conditional instability of the second kind) on the vertical distribution of cumulus heating is examined by expanding the vertical heating profile into its Fourier series with Fourier coefficients f1, f2, . . . , fN. In the standard analysis presented, N = 8 is used. The use of eight Fourier terms provides an adequate vertical resolution considering the current state of knowledge of the dependence of cumulus heating profiles on environmental conditions.
The results of the analyses are illustrated in the stability diagrams in the parameter space of Fourier coefficients, showing regions of stability and instability. These results show that all Kelvin wave solutions are stable when the heating parameter ε is smaller than a critical value εc, the precise value of which depends on how the Fourier coefficients, fn, decrease with n. For moderately large values of the heating parameter (say, for ε ≥ 2), Kelvin wave solutions become unstable for sufficiently negative values of f2. The authors found that the stability diagrams of Rossby waves are identical to those of Kelvin waves.
If the Fourier coefficients fn decrease rapidly with n, negative values of f2 mean the heating profiles have a maximum in the upper troposphere. An examination of the composition of the apparent heat source due to cumulus clouds indicates that for moderately large amounts of total precipitation equatorial Kelvin waves and Rossby waves are more likely to be unstable through the wave-CISK mechanism if the clouds are very vigorous, so that the convergence of the eddy heat flux has a maximum in the upper troposphere.
Corresponding author address: Dr. Han-Ru Cho, Department of Physics, University of Toronto, 60 St. George Street, Toronto, ON M5S 1A7 Canada.
Email: cho@physics.utoronto.ca
