  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 parameterised 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 model of Kuhfuss
(1986) 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 $20
M_\odot$ progenitor to further illustrate problems of 1D turbulence models. If
the buoyant driving term is formulated in a conservative manner, the explosion
energy of $\mathord{\sim}2\times 10^{51}\, \mathrm{erg}$ for the corresponding
non-conservative turbulence model is reduced to $<10^{48}\,\mathrm{erg}$ 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 multi-dimensional 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.
