  Our understanding of the core-collapse supernova explosion mechanism is
incomplete. While the favoured scenario is delayed revival of the stalled shock
by neutrino heating, it is difficult to reliably compute explosion outcomes and
energies, which depend sensitively on the complex radiation hydrodynamics of
the post-shock region. The dynamics of the (non-)explosion depend sensitively
on how energy is transported from inside and near the proto-neutron star (PNS)
to material just behind the supernova shock. Although most of the PNS energy is
lost in the form of neutrinos, hydrodynamic and hydromagnetic waves can also
carry energy from the PNS to the shock. We show that gravity waves excited by
core PNS convection can couple with outgoing acoustic waves that present an
appreciable source of energy and pressure in the post-shock region. Using
one-dimensional simulations, we estimate the gravity wave energy flux excited
by PNS convection and the fraction of this energy transmitted upward to the
post-shock region as acoustic waves. We find wave energy fluxes near
$10^{51}\,\mathrm{erg}\,\mathrm{s}^{-1}$ are likely to persist for
$\sim1\,\mathrm{s}$ post-bounce. The wave pressure on the shock may exceed
$10\%$ of the thermal pressure, potentially contributing to shock revival and,
subsequently, a successful and energetic explosion. We also discuss how future
simulations can better capture the effects of waves, and more accurately
quantify wave heating rates.
