  We propose a regularization for Reduced Order Models (ROMs) of the
quasi-geostrophic equations (QGE) to increase accuracy when the Proper
Orthogonal Decomposition (POD) modes retained to construct the reduced basis
are insufficient to describe the system dynamics. Our regularization is based
on the so-called BV-alpha model, which modifies the nonlinear term in the QGE
and adds a linear differential filter for the vorticity. To show the
effectiveness of the BV-alpha model for ROM closure, we compare the results
computed by a POD-Galerkin ROM with and without regularization for the
classical double-gyre wind forcing benchmark. Our numerical results show that
the solution computed by the regularized ROM is more accurate, even when the
retained POD modes account for a small percentage of the eigenvalue energy.
Additionally, we show that, although computationally more expensive that the
ROM with no regularization, the regularized ROM is still a competitive
alternative to full order simulations of the QGE.
