sinusoidal oscillations of exponentially growing amplitude. While in models without heating the SASI grows in amplitude until oscillations saturate while keeping its characteristic period (e.g., @FT09a), in models with significant heating this period increases when the amplitude becomes large, and eventually the regularity of the oscillation is lost.

![Same as Figure \[f:shock\_entropy\_sasi\], but for convection-dominated models that bracket the threshold for explosion (e3B06 and e3B08). Even though $\ell=1$ shock oscillations have no clear periodicity, the relation between destruction of high-entropy bubbles and large amplitude shock sloshings is still present. The unit of length is the initial shock radius without heating $r_{\rm s0}$ and the unit of time is the free-fall time at this position ($\sim 3$ ms for a central mass of $1.3M_\sun$ and $r_{\rm s0}\sim 150$ km, §\[s:setup\]).[]{data-label="f:shock_entropy_conv"}](f4.eps){width="\columnwidth"}

This breakdown of the SASI cycle is due to large-scale, long-lived fluid parcels with enhanced entropy emerging in the post-shock region. These structures are seeded during shock expansions (Figure \[f:shock\_entropy\_snapshots\]a; see also @scheck08). For small shock displacements, these elongated bubbles are shredded by lateral flows inherent in the SASI, and are advected out of the gain region, allowing the advective-acoustic cycle to proceed as in the case without heating. Above a 