  In this paper, we propose a nonintrusive filter-based stabilization of
reduced order models (ROMs) for uncertainty quantification (UQ) of the
time-dependent Navier-Stokes equations in convection-dominated regimes. We
propose a novel high-order ROM differential filter and use it in conjunction
with an evolve-filter-relax algorithm to attenuate the numerical oscillations
of standard ROMs. We also examine how stochastic collocation methods (SCMs) can
be combined with the evolve-filter-relax algorithm for efficient UQ of fluid
flows. We emphasize that the new stabilized SCM-ROM framework is nonintrusive
and can be easily used in conjunction with legacy flow solvers. We test the new
framework in the numerical simulation of a two-dimensional flow past a circular
cylinder with a random viscosity that yields a random Reynolds number with mean
$Re=100$.
