  Earth's tropics are characterized by quasi-steady precipitation with small
oscillations about a mean value, which has led to the hypothesis that moist
convection is in a state of quasi-equilibrium (QE). In contrast, very warm
simulations of Earth's tropical convection are characterized by
relaxation-oscillator-like (RO) precipitation, with short-lived convective
storms and torrential rainfall forming and dissipating at regular intervals
with little to no precipitation in between. We develop a model of moist
convection by combining a zero-buoyancy model of bulk-plume convection with a
QE heat engine model, and we use it to show that QE is violated at high surface
temperatures. We hypothesize that the RO state emerges when the equilibrium
condition of the convective heat engine is violated, i.e., when the net cooling
times a thermodynamic efficiency exceeds the work that can be performed. We
test our hypothesis against one- and three-dimensional numerical simulations
and find that it accurately predicts the onset of RO convection. The proposed
mechanism for RO emergence from QE breakdown is agnostic of the condensing
component, and can be applied to any planetary atmosphere undergoing moist
convection. To date, RO states have only been demonstrated in three-dimensional
convection-resolving simulations, which has made it seem that the physics of
the RO state requires simulations that can explicitly resolve the
three-dimensional interaction of cloudy plumes and their environment. We
demonstrate that RO states also exist in single-column simulations of
radiative-convective equilibrium with parameterized convection, albeit in a
different surface temperature range and with much longer storm-free intervals.
