Dynamics of Tropical Low-Frequency Waves: An Analysis of the Moist Kelvin Wave

Stability of the equatorial atmosphere to a quasi-zonal, low frequency (order of 10−6 s−1) disturbance is investigated, using a model that consists of a two-layer free atmosphere and well-mixed boundary layer. The inclusion of boundary layer convergence leads to a circulation-dependent heating more nearly in accord with the behavior of numerically simulated low-frequency waves. Slowly eastward moving unstable waves were found in a parameter regime stable to inviscid wave-CISK. The instability depends crucially upon the vertical distribution of the moist static energy of the basic state. A derived instability criterion suggests that amplification occurs when the condensational heating supported jointly by interior wave convergence and frictional convergence dominates over the dissipations due to longwave radiation and boundary layer viscosity. The unstable waves exhibit preferred planetary scales. Since the vertical distribution of moist static energy of the basic state is closely related to sea surface temperature (SST), with increasing SST the growth rate increases for all wavelength, but the preferred scales shifts to shorter wavelength. The boundary layer convergence plays an important role in spatial scale selection. It not only suppresses unbounded growth of short waves, but also couples barotropic and baroclinic components in such a way that the generation of wave available potential energy is most efficient for planetary scales. In the presence of boundary layer friction, the amplitude of an unstable wave in the zonal wind (or geopotential) at the upper level is significantly larger than that at the lower level. The phases between the two levels differ by about 180°. The slow eastward movement results mainly from the interior wave-induced reduction of static stability and thermal damping. Behaviors of model unstable waves appear to resemble the observed 40–50 day mode in many aspects, such as vertical structure, energy source, zonal phase propagations, characteristic zonal and meridional scales, and its relation to SST. Limitations of the model are also discussed.