It is shown that the complexity of turbulence can be reduced by a three-point closure. Based on this result the picture of a cascade of turbulence can be expressed by stochastic processes, which can be described by Fokker-Planck equations. This compact description is derived from the analysis of experimental data. Even a Fokker-Planck equation can be estimated directly from experimental data. This stochastic description allows also to set the complexity of turbulence in the context of non-equilibrium thermodynamics. In particular we show that the generalized entropy relation, namely the so-called integral fluctuation theorem [1], is valid and can be considered as a new basic law for turbulence. Consequences of the integral fluctuation theorem are that the scaling properties of turbulence are violated, that even small scale features of turbulence still carry some non universal signatures of large scale generating processes and that extreme velocity fluctuations are based on events of negative entropy production.

At last it is shown that method of analyzing and characterizing turbulent data can be used also for wave data from oceans. Here it will be discussed that freak or rogue waves, commonly described by deterministic models like the nonlinear Schroedinger equation or an focusing effect, can be grasped alternatively by this stochastic cascades approach.

[1] Seifert, U. : Stochastic thermodynamics, fluctuation theorems and molecular machines. Rep. Prog. Phys. 75, 126001 (2012)

Contact : michele.moucot@cea.fr