Direct Numerical Simulations of the Navier-Stokes Alpha Model

Abstract

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.