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

We consider the Navier-Stokes-ω¯ model, given byut−u×ω¯−νΔu+∇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.