  Thermonuclear flashes of hydrogen and helium accreted onto neutron stars
produce the frequently observed Type I X-ray bursts. It is the current paradigm
that almost all material burns in a burst, after which it takes hours to
accumulate fresh fuel for the next burst. In rare cases, however, bursts are
observed with recurrence times as short as minutes. We present the first
one-dimensional multi-zone simulations that reproduce this phenomenon. Bursts
that ignite in a relatively hot neutron star envelope leave a substantial
fraction of the fuel unburned at shallow depths. In the wake of the burst,
convective mixing events driven by opacity bring this fuel down to the ignition
depth on the observed timescale of minutes. There, unburned hydrogen mixes with
the metal-rich ashes, igniting to produce a subsequent burst. We find burst
pairs and triplets, similar to the observed instances. Our simulations
reproduce the observed fraction of bursts with short waiting times of ~30%, and
demonstrate that short recurrence time bursts are typically less bright and of
shorter duration.
