High-resolution global simulations over zonally symmetric aqua planets are examined using Fourier analysis in the zonal direction. We highlight the tropics, where the large-scale weather consists of convectively-coupled waves so that explicit convection is an especially topical novelty.Squared differences between pairs of runs grow from initially tiny values to saturation at twice the climatological variance. For wavelengths shorter than 103 km, differences saturate within about a day. For tropical long waves, the time to saturation indicates predictability for at least 2 weeks. This time scale is similar in middle latitude flow, which interacts with tropical waves in the 3D model, but it is also similar in 2D pseudo-equatorial vertical plane simulations of pure convectively coupled gravity waves. As a result, no simple conclusions can be drawn about whether tropical predictability is limited more by tropical chaos or by tropical-extratropical interactions.Difference growth appears to fill out the saturation energy spectrum in a “vertical” (up-magnitude) rather than “horizontal” (up-scale) manner. Up-scale growth thus occurs as a continuing amplification of large scales after small scales saturate, which begs the question of what sets the shape of the saturation (climatological) power spectra. Wind spectra are nearly power-law with a logarithmic slope of about -5/3 in the free troposphere, remarkably so in the 2D runs and clearly distinct from slope -2 (a null hypothesis of spectrally white wind divergence). A common interpretation of -5/3 slope - as indicative of a cascade, a steady conservative transfer of energy from source to sink scales by interactions that are local in log-wavelength space - is hard to apply to these moist tropical waves.