Existence of smooth attractors for the Navier–Stokes-omega model of turbulence

We consider the Navier–Stokes- ω ¯ model, given by u t − u × ω ¯ − ν Δ u + ∇ P = f , ω = ∇ × u , ∇ ⋅ u = 0 subject to periodic boundary conditions with zero mean. The NS- ω ¯ model is an outgrowth of ideas in approximate deconvolution models and in NS-alpha models. Like the NS-alpha model, it is simple and conserves, in the appropriate context, kinetic energy and helicity (3d) or energy and enstrophy (2d). In first tests NS- ω ¯ was found to be accurate, robust and amenable to efficient numerical simulation. In this note we prove existence and regularity of a global attractor for the model.