  Kolmogorov's theory of turbulence predicts that only wavenumbers below some
critical value, called Kolmogorov's dissipation number, are essential to
describe the evolution of a three-dimensional fluid flow. A determining
wavenumber, first introduced by Foias and Prodi for the 2D Navier-Stokes
equations, is a mathematical analog of Kolmogorov's number. The purpose of this
paper is to prove the existence of a time-dependent determining wavenumber for
the 3D Navier-Stokes equations whose time average is bounded by Kolmogorov's
dissipation wavenumber for all solutions on the global attractor whose
intermittency is not extreme.
