  According to Burrows et al.'s acoustic mechanism for core-collapse supernova
explosions, the primary, l=1, g-mode in the core of the proto-neutron star is
excited to an energy of ~ 10^{50} ergs and damps by the emission of sound
waves. Here we calculate the damping of the primary mode by the parametric
instability, i.e., by nonlinear, 3-mode coupling between the low-order primary
mode and pairs of high-order g-modes. We show that the primary mode is strongly
coupled to highly resonant, neutrino damped pairs with n>10; such short
wavelength interactions cannot be resolved in the simulations. We find that the
parametric instability saturates the primary mode energy at ~10^{48} ergs, well
below the energy needed to drive an explosion. We therefore conclude that
acoustic power is unlikely to be energetically significant in core-collapse
supernova explosions.
