  Spatial filtering has been central in the development of large eddy
simulation reduced order models (LES-ROMs) and regularized reduced order models
(Reg-ROMs), In this paper, we perform a numerical investigation of spatial
filtering. To this end, we consider one of the simplest Reg-ROMs, the Leray ROM
(L-ROM), which uses ROM spatial filtering to smooth the flow variables and
decreases the amount of energy aliased to the lower index ROM basis functions.
We also propose a new form of ROM differential filter and use it as a spatial
filter for the L-ROM. We investigate the performance of this new form of ROM
differential filter in the numerical simulation of a flow past a circular
cylinder at a Reynolds number $Re=760$.
