Two-dimensional versus three-dimensional supernova hydrodynamic instability growth

Numerical simulations using the SN hydrodynamics code PROMETHEUS are carrie d out to study the difference between growth of two-dimensional versus thre e-dimensional single-mode perturbations at the He-H and O-He interfaces of SN 1987A. We find that in the rest frame of an unperturbed one-dimensional interface, a three-dimensional single-mode perturbation grows approximate t o 30%-35% faster than a two-dimensional single-mode perturbation, when the wavelengths are chosen to give the same linear stage growth in the planar l imit. In simulations where we impose single-mode density perturbations in t he O layer of the initial model and random velocity perturbations in the po stshock fluid near the He-H interface, we find that both axisymmetric O spi kes and three-dimensional O spikes penetrate significantly further than two -dimensional O spikes. The difference between two dimensions and three dime nsions predicted by our calculations is not enough to account for the diffe rence between observed Co-56 velocities in SN 1987A and the results of prev ious two-dimensional simulations of SN 1987A, but our results suggest that the real three-dimensional hydrodynamics are noticeably different than the two-dimensional simulations predict.