evolution of convection-dominated models is illustrated by Figure \[f:shock\_entropy\_conv\]. Entropy enhancements are initially generated by convection. Bubbles grow and merge into large-scale structures, which cause non-linear shock displacements. In non-exploding models, bubbles have a short lifetime, and hence the shock undergoes sloshings of moderate amplitude over a range of temporal frequencies. Note that the destruction of large bubbles can also lead to shock sloshings, but the persistent generation of entropy fluctuations of smaller scale and amplitude prevent the emergence of SASI oscillations with a well-defined periodicity.

For high enough heating rate, large bubbles are able to survive for many eddy turnover times, leading to explosion in a manner similar to that of SASI-dominated models. The role of high-entropy bubbles in convection-dominated models has been documented previously [@dolence2013; @couch2012].

![Time-series diagnostics for exploding models with different initial perturbations (Table \[t:models\]). Top panels show average shock radius, middle panels show $\ell=1$ shock Legendre coefficient, and bottom panel shows fraction of the postshock volume with entropy higher than unity. Note the longer time to explosion and late onset of $\ell=1$ oscillations in models with even $\ell$ perturbations (p0B10L2 and p0B10G4). The unit of length is the initial shock radius without heating $r_{\rm s0}$ 