A critical assessment of turbulence models for 1D core-collapse supernova simulations

It has recently been proposed that global or local turbulence models can be used to simulate core-collapse supernova explosions in spherical symmetry (1D) more consistently than with traditional approaches for parametrized 1D models. However, a closer analysis of the proposed schemes reveals important consistency problems. Most notably, they systematically violate energy conservation as they do not balance buoyant energy generation with terms that reduce potential energy, thus failing to account for the physical source of energy that buoyant convection feeds on. We also point out other non-trivial consistency requirements for viable turbulence models. The Kuhfuss model from the 1980s proves more consistent than the newly proposed approaches for supernovae, but still cannot account naturally for all the relevant physics for predicting explosion properties. We perform numerical simulations for a $20 \, \mathrm{M}_\odot$ progenitor to further illustrate problems of 1D turbulence models. If the buoyant driving term is formulated in a conservative manner, the explosion energy of ${\sim }2\times 10^{51}\, \mathrm{erg}$ for the corresponding non-conservative turbulence model is reduced to $\lt 10^{48} \, \mathrm{erg}$ even though the shock expands continuously. This demonstrates that the conservation problem cannot be ignored. Although plausible energies can be reached using an energy-conserving model when turbulent viscosity is included, it is doubtful whether the energy budget of the explosion is regulated by the same mechanism as in multidimensional models. We conclude that 1D turbulence models based on a spherical Reynolds decomposition cannot provide a more consistent approach to supernova explosion and remnant properties than other phenomenological approaches before some fundamental problems are addressed.