Here is my current title and abstract. I’ve also added it to a href=”http://www.joeandersen.com/publications”my publications page/a (Doubling the number of entries there!)br /br /span style=”font-weight: bold;”A toy model of the instability in the equatorially trapped convectively coupled waves on the equatorial beta plane; /spanbr /span style=”font-weight: bold;”J. A. Andersen and Z. Kuang /spanbr /span style=”font-weight: bold;”JAS, Submitted, 2008. /spanbr /br /span style=”font-weight: bold;”Abstract/span: The equatorial atmospheric variability shows a spectrum of significant peaks in the wavenumber-frequency domain. These peaks have been identified with the equatorially trapped wave modes of rotating shallow water wave theory. This paper addresses the observation that the various wave types (e.g. Kelvin, Rossby, etc) and wavenumbers show differing powers. It is hypothesized that this is due to variations in the linear stability of the atmosphere to the various wavetypes depending on both the specific wave type and the wavenumber. A simple model of the convectively coupled waves on the equatorial beta plane is constructed. The linear instability of this system is evaluated by eigenvalue analysis. This analysis shows unstable waves with phase speeds, growth rates, and structures (vertical and horizontal) that are broadly consistent with the results from cloud system resolving simulations and observations. The linear system shows peak unstable Kelvin waves around zonal wavenumber seven with peak growth rates of ~0.08/day (e-folding time of ~13 days). The system also shows unstable Mixed Rossby-Gravity (MRG) and Inertio-Gravity waves with significant growth in the zonal wavenumber range from negative (westward phase speed) fifteen to positive (eastward phase speed) ten. The peak MRG growth rate is around one third that of the Kelvin wave and occurs at zonal wavenumber three. The Rossby waves in this system are stable, and the Madden-Julian Oscillation is not observed. While the instability spectrum is found to depend on the Inter-Tropical Convergence Zone configuration in the model, it is shown that the differing instabilities of the different wave modes are related to their different efficiency in converting input energy into divergent flow. This energy conversion efficiency difference is suggested as a factor that helps to shape the observed wave spectrum.