Complex systems like turbulence and ocean waves can produce extreme events like large changes in wind speed or monster waves. It has long been debated whether coherent structures or special statistical proper- ties are essential for the understanding. Here we show a comprehensive stochastic approach for Lagrangian and Eulerian turbulence, as well as, for waves, leading to a joint multi-point statistic. We consider cascade trajectories through scales as realizations of a stochastic Langevin process that can be deduced from data. Knowledge of the stochastic equations allows determination of the entropy production of each cascade trajectory. Trajectories with negative entropies are linked to large fluctuations like extreme wind speeds or monster waves. Thus entropy seems to select different structures. Furthermore, negative and posi- tive entropy values are balanced by rigorous fluctuation theorems, so that extreme and normal fluctuations are mutually dependent. In this way the entropy concept links statistics with the coherent structure approach. Finally, trajectories concentrate around an optimal path, called instanton, which is the minimum of an effective action given by the estimated stochastic equations. Entropons, defined as instantons conditioned on fixed entropy values, pinpoint the trajectories responsi- ble for the emergence of non-Gaussian statistics at small scales.
References:
Ann. Rev. Cond. Matt. Phys. 10, 107-132 (2019)
EPL 137, 53001 (2022)
Phys. Rev. Lett. 129, 034502 (2022)