Ideal Turbulence

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. A mathematically rigorous definition of ideal turbulence is based on standard notions of dynamical systems theory and chaos theory. Ideal turbulence is observed in various idealized models of real distributed systems of electrodynamics, acoustics, radiophysics, etc. In systems without internal resistance, cascade processes are capable to birth structures of arbitrarily small scale and even to cause stochastization of the systems. Just these phenomena are inherent in ideal turbulence and they help to understand the mathematical scenarios for many features of real turbulence.