Convectively coupled wave–environment interactions

In the tropical atmosphere, waves can couple with water vapor and convection to form large-scale coherent structures called convectively coupled waves (CCWs). The effects of water vapor and convection lead to CCW–mean flow interactions that are different from traditional wave–mean flow interactions in many ways. 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 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. The basic interaction mechanisms are that the mean flow’s vertical shear determines the preferred propagation direction of the CCW, and the CCWs can drive changes in the mean shear through convective momentum transport, with energy transfer that is sometimes upscale and sometimes downscale. 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.