Using systematic multiscale asymptotics, Majda and Klein arrived at an asymptotic closure for the ideal fluid equations governing dynamics on large scales in the tropical atmosphere. In collaboration with Majda, we considered a plausible model for smaller scale flows in the tropics and are able to calculate the structure of the Madden-Julian oscillation; this is a planetary scale organization of winds,the understanding of which has been called "the holy grail" of tropical meteorology.

In a second problem, we studied the equatorial primitive
equations over longer time and spatial scales. The resultant coupled nonlinear dispersive equations for the amplitudes of interacting wave packets are novel both from the perspective of the atmospheric sciences and from a more general mathematical setting. These equations describe the influence of large scale tropical waves on midlatitude waves and, in particular, are relevant for understanding the effect of the Madden-Julian oscillation on midlatitude weather. I will also discuss the Hamiltonian structure of these waves and show that they admit some analytic solitary wave solutions.