On the ensemble average in the study of approximate inertial manifolds, II

In this note we obtained a new time averaged estimate of the distance between the orbit generated by solutions of 2-D Navier-Stokes equations and one of its approximate inertial manifolds in the space periodic case, using the Gevrey class regularity of the solutions in the space periodic case. This estimate is a substantial improvement of the author's previous one in the “very” high wave modes, or, physically, far in the dissipation range of turbulence.