A combined wind tunnel and computational study of grid-generated turbulence along the centreline shows that the close to -5/3 power law signature of energy spectra in the frequency domain originates in the production region close to the grid where the velocity derivative statistics become quite suddenly isotropic but also where the turbulent fluctuating velocities are very intermittent and non-Gaussian. As the inlet flow velocity increases, these power laws are increasingly well defined and increasingly close to -5/3 over an increasing range of frequencies. However, this range continuously decreases with streamwise distance from the grid even though the local Reynolds number first increases and then decreases along the same streamwise extent. The intermittency at the point of origin of the close to -5/3 power spectra consists of alternations between intense vortex tube clusters with shallow broad-band spectra and quiescent regions where the velocity fluctuations are smooth with steep energy spectra.