We present an experimental study of the typical time scales of spatial Fourier modes of the vorticity in turbulence. The measurements of time auto-correlation functions, for well defined spatial wavenumbers $k$, reveal that vorticity exhibits two characteristic times: a short one depending on the inverse of the wavenumber, which can be interpreted as a manifestation of the sweeping effect (random advection), and a larger one, independent of k, of the order of the integral time scale of the flow. In a second step, we show that two different vorticity Fourier modes with wavenumbers $k$ and $k′$ are long-time cross-correlated, whatever the spectral gap $k−k′$. The existence of a significant cross-correlation between scales, indicates a strong statistical dependance between scales, at variance with the original Kolmogorov theory (1941). This long-time correlation, closely related to the integral forcing time, could be ascribed to some evidence of time intermittency, associated with fluctuations in time of the energy injected at large scales and resulting in a lack of global scale invariance of the dynamical properties of the turbulent flow.