Abstract A wide range of the observed variability in the ITCZ is frequently explained in terms of equatorially trapped modes arising from Matsuno’s linear shallow-water model. Here, a series of zonally constant, meridionally symmetric aquachannel WRF simulations are used to study the propagation of tropical cloud clusters (CCs; patches of deep cloudiness and precipitation) in association with eastward-moving super cloud clusters (SCCs), also called convectively coupled Kelvin waves (CCKWs). Two independent but complementary methods are used: the first, from a local approach, involves a CC-tracking algorithm, while the second uses Lagrangian trajectories in a nonlocal framework. We show that the large-scale flow in low to midlevels advects the CCs either eastward or westward depending on model climatology, proximity to the CCKW axis, and latitude. Moreover, for most analyzed cases, sequences of CCs oscillate, describing qualitatively sinusoidal-like paths in longitude–time space, although with sharp transitions from westward to eastward motion due to westerly wind burst activity associated with the CCKWs. We also find that the discrete precipitation elements (CCs) are embedded in continuous tracks of positive moisture anomalies, which are parallel to the Lagrangian trajectories themselves. A conceptual model of the nonlinear SCC–CC interaction is presented.