There is a clear distinction between simple laminar and complex turbulent fluids. But in some cases, as for the nocturnal planetary boundary layer, a stable and well-ordered flow can develop intense and sporadic bursts of turbulent activity which disappear slowly in time. This phenomenon is ill-understood and poorly modeled; and yet, it is central to our understanding of weather and climate dynamics. We present here a simple model which shows that in stably stratified turbulence, the stronger bursts can occur when the flow is expected to be more stable. The bursts are generated by a rapid non-linear amplification of energy stored in waves, and are associated with energetic interchanges between vertical velocity and temperature (or density) fluctuations. Direct numerical simulations on grids of 2048 3 points confirm this somewhat paradoxical result of measurably stronger events for more stable flows, displayed not only in the temperature and vertical velocity derivatives, but also in the amplitude of the fields themselves.PACS numbers: 47.55. Hd, 47.35.Bb, 47.27.ek Large fluctuations are common in physical systems with long-range correlations, and have been found to be linked to so-called "1/f" noise [1]. They take the form of sporadic and localized events, as observed in many instances in critical phenomena and in turbulent flows, and are diagnosed through non-Gaussian Probability Distribution Functions (PDFs) [2]. In turbulence, strong events occur in field gradients, with the velocity itself being nearly Gaussian. There are however exceptions to this last rule for shear flows [3,4], quantum fluids [6,7], and subtropical current systems [5]. Extreme events associated with random plumes have also been diagnosed in the atmospheric convective boundary layer [8], or when linked with coherent structures, e.g., storm tracks.The occurrence of intermittent strong activity is a signature of fully developed turbulence and is therefore more surprising in stable flows. Intermittency makes the stable nocturnal planetary boundary layer (PBL) highly unpredictable: as night sets in, this layer between the atmosphere and land or sea stabilizes due to the radiative cooling of the land and ocean masses. It is still unclear how stable the nocturnal PBL becomes. Three regimes have been observed [9]: very stable, weakly stable with turbulent motions persisting and competing with internal gravity waves, and transitory. Even in the very stable case, the PBL is subject to intense sporadic bursts of turbulence which die out after many wave periods [9,10].Numerical simulations play an increasing role in the understanding of these complex processes, and in quantifying the dual problem of the increased stability [11] and the spontaneous generation of bursts. However, modeling of the PBL in weather and climate codes is often inadequate, resulting, for example, in an inaccurate evaluation of the extension of the ice sheet, as is the case over Greenland [12], and in a faulty estimate of the overall energy balance in long-term climate syste...