A simple nonlinear model of low frequency (interseasonal) oscillations in the tropical atmosphere

Abstract. In this paper, for a prescribed normalized vertical convective heating profile, nonlinear Kelvin wave equations with wave-CISK heating over equatorial region is reduced to a sixth-order nonlinear ordinary differential equation by using the Galerkin spectral method in the case of considering nonlinear interaction between first and second baroclinic modes. Some numerical calculations are made with the fourth- order Rung-Kutta scheme. It is found that in a narrow range of the heating intensity parameter b, 30-60-day oscillation can occur through linear coupling between first and second baroclinic Kelvin wave-CISK modes for zonal wave-number one when the convective heating is confined to the lower and middle tropospheres. While for zonal wavenumber two, 30-60-day oscillation can be observed in a narrow range of b only when the convective heating is confined to the lower troposphere. However, in a wider range of this heating intensity parameter, 30-60-day oscillation can occur through nonlinear interaction between the first and second baroclinic Kelvin wave-CISK modes with zonal wavenumber one for three vertical convective heating profiles having a maximum in the upper, middle and lower tropospheres, and the total streamfield of the nonlinear first and second baroclinic Kelvin wave-CISK modes possesses a phase reversal between the upper- and lower-tropospheric wind fields. While for zonal wavenumber two, no 30-60-day oscillations can be found. Therefore, it appears that nonlinear interaction between vertical Kelvin wave-CISK modes favours the occurrence of 30-60-day oscillations, particularly, the importance of the vertical distribution of convective heating is re-emphasised.