We simulate the Madden-Julian oscillation (MJO) over an aquaplanet with uniform surface temperature using the multiscale modeling framework (MMF) configuration of the Energy Exascale Earth System Model (E3SM-MMF). The model produces MJO-like features that have a similar spatial structure and propagation behavior to the observed MJO. To explore the processes involved in the propagation and maintenance of these MJO-like features, we perform a vertically resolved moist static energy (MSE) analysis for the MJO. Unlike the column-integrated MSE analysis, our method emphasizes the local production of MSE variance and quantifies how individual physical processes amplify and propagate the MJO’s characteristic vertical structure. We find that radiation, convection, and boundary layer processes all contribute to maintaining the MJO, balanced by the large-scale MSE transport. Furthermore, large-scale dynamics, convection, and boundary layer processes all contribute to the propagation of the MJO, while radiation slows the propagation. Additionally, we perform mechanism-denial experiments to examine the role of radiation and associated feedbacks in simulating the MJO. We find that the MJO can still self-emerge and maintain its characteristic structures without radiative feedbacks. This study highlights the role of convective MSE transport in the MJO dynamics, which was overlooked in the column-integrated MSE analysis.