CCW-mean flow interactions are studied here in two types of models: a multiscale model that represents CCW structures in two spatial dimensions directly above the Earth's equator, and an amplitude model in the form of ordinary differential equations (ODEs) for the CCW and mean flow amplitudes. The amplitude equations are shown to capture the qualitative behavior of the spatially resolved model, including nonlinear oscillations and a Hopf bifurcation as the climatological background wind is varied. Furthermore, an even simpler set of amplitude equations can also capture some of the essential oscillatory behavior, and it is shown to be equivalent to the Duffing oscillator.
In addition to CCW-mean flow interactions, also discussed are CCW-water vapor interactions, which form the basis of the Madden Julian Oscillation (MJO) skeleton model of the first two authors. The key parameter of the MJO skeleton model is estimated theoretically and is in agreement with previously conjectured values.
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