  In the literature on projection-based nonlinear model order reduction for
fluid dynamics problems, it is often claimed that due to modal truncation, a
projection-based reduced-order model (PROM) does not resolve the dissipative
regime of the turbulent energy cascade and therefore is numerically unstable.
Efforts at addressing this claim have ranged from attempting to model the
effects of the truncated modes to enriching the classical subspace of
approximation in order to account for the truncated phenomena. This paper
challenges this claim. Exploring the relationship between projection-based
model order reduction and semi-discretization and using numerical evidence from
three relevant flow problems, it argues in an orderly manner that the real
culprit behind most if not all reported numerical instabilities of PROMs for
turbulence and convection-dominated turbulent flow problems is the Galerkin
framework that has been used for constructing the PROMs. The paper also shows
that alternatively, a Petrov-Galerkin framework can be used to construct
numerically stable PROMs for convection-dominated laminar as well as turbulent
flow problems that are numerically stable and accurate, without resorting to
additional closure models or tailoring of the subspace of approximation. It
also shows that such alternative PROMs deliver significant speedup factors.
