Presented is a nonlinear dynamical model of MJO-like systems simulated by the Grabowski (2001) super-parameterization, where cloud-system-resolving models represent convection explicitly rather than a conventional convective parameterization scheme. The dynamical model is conceptualized as two coupled stationary coherent circulations: mesoscale convective systems and equatorial Rossby-gyres. These circulations are coupled exactly by an inter-scale mapping and transformations among dimensionless bulk quantities that represent the energy available to convection organized on mesoscales, Rossby-gyre dynamics and the effect of the surface pressure gradient on the propagation of the coupled system. This representation reduces to an archetypal form in which the normalized propagation speed is the sole bulk quantity. Despite this drastic simplification, the archetypal model represents key properties such as dynamical structure, meridional and vertical momentum transport and atmospheric super-rotation realized by the super-parameterization. The novelty of the archetype is its simple representation of organized convection, whose effects are prominently manifested as mesoscale momentum transport. Finally, basic issues facing both super-parameterization and traditional parameterization in regard to the multiscale organization of tropical convection are discussed.