Rigorous bounds on intermittent bursts for turbulent flows

It is known that several quantities associated to the small scales in turbulent flows tend to be almost stationary in time except for the occurrence of sporadic bursts. We prove that these bursts must satisfy certain bounds related to the large-scale flow: the amplitude of bursts decreases at least exponentially with the cut-off frequency, and a fixed time before the burst the size of the large-scale enstrophy must have a size depending at least exponentially on the number of oscillations of the burst. The result applies as well to magnetohydrodynamic flows.