We present a three-dimensional minimal model that produces a self-sustained quasi-biennial oscillation (QBO)-like oscillation in a radiative–moist convective quasi-equilibrium state. The computational domain is rectangular 640 km × 160 km one with doubly periodic boundary conditions. After initial transition time, an oscillation with a period of about 300 days emerges in the stratosphere, both in the domain-averaged zonal wind and meridional wind. A synchronization of the zonal and meridional winds is observed. It is characterized as an anti-clockwise rotation of a skewed spiral feature with height in the horizontal mean wind vectors.

The penetration of the QBO-like wind oscillations into the troposphere occurs similar to the counterpart of two-dimensional minimal model as found by Yoden et al. (2014), Nishomoto et al. (2016) and Bui et al. (2017). Modulations of the tropospheric temperature anomaly and smoothed precipitation are also noted with irregular periods of about 100 days, in which heavy precipitation is associated with positive temperature anomaly. Fine temporal outputs of the simulation with 5 minutes reveal three types of precipitation patterns: isolated quasi-stationary type clusters, fast-moving back-building type, and fast-moving squall-line type patterns. The quasi-stationary type clusters are newly identified with this three-dimensional model. Intermittent self-reorganization of convective systems into quasi-stationary type and transition back to the fast-moving back-building type or squall-line type are fundamental characteristics of self-aggregation in the proposed three-dimensional model framework.

The present three-dimensional minimal model of QBO-like oscillation could become a new test bed to investigate radiative–moist convective equilibrium states and possible downward influence of stratospheric processes to the moist convection and its organization in the tropical troposphere.