Title:
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PDEs and Asymptotics for the Tropical Atmosphere
Abstract:
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I shall discuss two new asymptotic regimes for
the nonlinear PDEs governing the tropical atmosphere.
Using systematic multiscale
asymptotics, we arrive at an asymptotic closure for
the ideal fluid equations governing dynamics on
large scales in the tropical atmosphere.
By selecting a plausible analytic
model for smaller scale flows
in the tropics, we predict the
large scale 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 the second problem, we study the same equations,
but 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. Furthermore, the
amplitude equations have a Hamiltonian structure and admit
analytic solitary wave solutions.