The nonlinear evolution of unstable coupled equatorial ocean-atmosphere modes

Abstract

In this paper we investigate whether observed intraseasonal variability in the equatorial Pacific can be attributed to finite amplitude waves resulting from unstable air-sea interactions. Within a Zebiak - Cane type model of the coupled equatorial ocean - atmosphere, the nonlinear equilibration of instabilities of a simple basic state is considered with periodic conditions on the ocean boundaries. Three mechanisms exist which can induce a finite amplitude equilibration on a time scale ε2t. Here t is the characteristic time scale of growth of the disturbance and ε the relative distance from the instability threshold. For each equilibration mechanism, the finite amplitude and period of the equilibrium state are computed as a function of ε and substantial amplitude can be reached for a reasonable degree of supercriticality. Thereafter the analysis is extended to include time-dependent external forcing. It is shown that interannual variability may result through the interaction of the response of a weak annual external forcing and the finite amplitude development of the intraseasonal instabilities.