Event-based complexity in turbulence

Since the studies of Kolmogorov and Oboukhov in 1941, the problem of in- termittent large velocity excursions was recognized to be one of the most intriguing and elusive aspects of turbulent flows. While many efforts were devoted since 1960s to the magnitude intermittency, related to the statistics of the large increments in the tur- bulent signals, the attention towards the so-called clustering intermittency has started to increase only in the last two decades, even if some pioneering studies were carried in previous years. The low attention towards the clustering intermittency is somewhat surprising, as intermittency itself is essentially defined as an alternance of extended qui- escent periods/regions and short/small high activity periods/zones. It is then natural to characterize intermittency by means of events marked along the dependent variable axes, whatever time or space. Conversely, the concept of crucial events and of temporal complexity, related to non-trivial clustering properties of these same events, has been proposed as a general interpretative framework for the investigation of complex systems with metastable self-organizing dynamics. Without any claim to being complete, in this chapter we give a review of event-based complexity approaches used in literature for the description of turbulence in the plane- tary boundary layer. The main goal is to put a first bridge between turbulence studies exploiting event-based complexity approaches, such as clustering exponents and classi- cal Oboukhov intermittency exponents, and studies about intermittent complex systems, where concepts and ideas developed in the fields of non-equilibrium statistical physics, probability theory and dynamical system theory are jointly exploited.