Convectively coupled wave-environment interactions

Simple models are presented for the interaction of convectively coupled waves (CCWs) with environmental wind shear or moisture. One of the main aims is to better understand convective momentum transport and energy transfers between CCWs and the mean flow: Under what circumstances is energy transfered upscale - i.e., from the CCWs to the mean flow, with acceleration of the mean flow? And under what circumstances is it downscale - i.e., decelerating the mean flow? In a simplified setting, these issues are essentially convectively coupled wave-mean flow interactions, which are different from traditional wave-mean flow interactions in several 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 (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.