A mechanism is presented, based on multiscale interactions via nonlinear wind-induced surface heat exchange (WISHE), that produces eastward-propagating, intraseasonal convective anomalies in the tropical atmosphere. Simulations of convectively coupled disturbances are presented in two intermediate-complexity atmospheric models. One is a shallow water model with a simple WISHE-motivated heating term. The other model is also based on a first baroclinic mode but has an additional prognostic equation for humidity and a simple representation of moist convection based on a quasi-equilibrium approximation. In spite of many differences between the models, they robustly produce a coherent signal in westerly winds and convection that travels eastward at 4–10 m s$^{-1}$. It is shown here that this slow signal is a forced response to an eastward-propagating Yanai (mixed Rossby–gravity) wave group. The response takes the form of a forced Kelvin wave that is driven nonlinearly, via WISHE, by meridional wind anomalies of the Yanai wave group and that travels considerably more slowly than the free convectively coupled Kelvin waves in these models. The Yanai waves are destabilized in the models used here by WISHE in the presence of mean easterlies, but more generally they could also be excited by stratiform instability in the absence of mean easterlies so that the mechanism described here could also operate without mean easterlies. Similarities to and differences from the Madden–Julian oscillation (MJO) and convectively coupled tropical waves are discussed.