Information capacity of turbulent cascades

The review will be given of the information-theory approach to turbulence. The main question is the following one: if non-equilibrium state has entropy lower than equilibrium at the same energy, where this information is encoded? We consider a general wave turbulence and show that its statistics cannot be close to Gaussian, that is, strictly speaking, weak wave turbulence does not exist. We also describe a set of resonantly interacting waves and respective shell model and describe its cascades and informational content.