  We explore the utility of the recently proposed alpha equations in providing
a subgrid model for fluid turbulence. Our principal results are comparisons of
direct numerical simulations of fluid turbulence using several values of the
parameter alpha, including the limiting case where the Navier-Stokes equations
are recovered. Our studies show that the large scale features, including
statistics and structures, are preserved by the alpha models, even at coarser
resolutions where the fine scales are not fully resolved. We also describe the
differences that appear in simulations. We provide a summary of the principal
features of the alpha equations, and offer some explanation of the
effectiveness of these equations used as a subgrid model for three-dimensional
fluid turbulence.
