Ideal turbulence: definition and models

Ideal turbulence is a mathematical phenomenon which occurs in certain infinite-dimensional deterministic dynamical systems, and implies that the attractor of a system lies off the phase space and among the attractor points there are fractal or even random functions. Ideal turbulence is observed in various idealized models of real distributed systems, addressed by electrodynamics, acoustics, radiophysics, etc. Unlike real systems, in ideal systems (without internal resistance), cascade processes are capable of giving birth to structures of arbitrarily small scale and even causing stochastization of the systems. Just these phenomena are readily described in the contest of ideal turbulence, and allows to understand the mathematical scenarios for many features of real turbulence. A mathematically rigorous definition of ideal turbulence is based on standard notions of dynamical systems theory and chaos theory.