In this talk we will show the global well-posedness of the three dimensional Navier-Stokes-alpha model (also known as a viscous Camassa-Holm equations). ... We will present semi-rigorous arguments showing that up to a certain wave number, in the inertial range, the translational energy power spectrum obeys the Kolmogorov power law for the energy decay of the three dimensional turbulent flow. ... This observation makes the Navier-Stokes-alpha model more computable than the Navier-Stokes equations. ...