  In this article, we present a mathematical theory of the Walker circulation
of the large-scale atmosphere over the tropics. This study leads to a new
metastable state oscillation theory for the El Nino Southern Oscillation
(ENSO), a typical inter-annual climate low frequency oscillation. The
mathematical analysis is based on 1) the dynamic transition theory, 2) the
geometric theory of incompressible flows, and 3) the scaling law for proper
effect of the turbulent friction terms, developed recently by the authors.
