| A simple theoretical model of the tropical troposphere is used to study whether boundary layer friction is destabilizing to the Madden-Julian Oscillation (MJO) and other convectively coupled moist equatorially trapped Kelvin-like modes. A linear stability analysis is performed on an equatorial beta-plane with a continuously stratified atmosphere using a Betts-Miller-like convective parameterization. The troposphere is divided into a frictional boundary layer close to the surface and a frictionless free troposphere. The basic state is horizontally homogeneous and uniformly convecting.;The full linear stability problem can be discretized into an eigenvalue problem that is barely computationally tractable. A scaling analysis appropriate for low frequency, long wavelength modes, such as the MJO, leads to a much simpler eigenvalue problem.;At issue is the manner in which surface momentum fluxes are distributed to the rest of the troposphere. We find, both though observations and model results, that a diffusive boundary layer is preferable to a well mixed boundary layer.;Friction is found to be modestly destabilizing for the moist Kelvin mode in both models, increasing its growth rate by 0.03 day-1 in the mixed-layer model and 0.01 day-1 in the eddy diffusion model. It also has a smaller destabilizing effect on the gravest moist Rossby mode. Frictionally forced boundary layer convergence promotes wave amplification by enhancing convective heating along the equator in the warm sector of the wave. With a radiation upper boundary condition, the longest waves have the largest growth rate. A rigid lid boundary condition slightly favors short wavelengths. |
