Wave CISK of Equatorial Waves and the Vertical Distribution of Cumulus Heating

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 e is smaller than a critical value ec, 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 e ≥ 2), Kelvin wave solutions become unstable for sufficiently n...