Turbulent models: problems and solutions

A.M.Mukhamedov

Kazan State Technical University of A.N.Tupolev's name

Tatarstan 9-15, Kazan, 420021, RUSSIA

New formalism for dealing with spatial inhomogeneous turbulence is given. The basic foundations are: 1) introducing of bundle spaces for representation of phase spaces of the stable turbulent regimes, 2) application of the non-holonomic Pfaff systems for definition of turbulent dynamics, 3) introducing of algebras and subalgebras of observable variables and their balance equations for specifying of the turbulent regimes and their appearances in several types of description compression. For example the low-dimensional attractors are considered for constructing of the lower stages of hierarchy of turbulent motions.

Previous unified schema proclaims a new research program in turbulence. In the context of information-driven systems it produces an attempt to reach the understanding of turbulent phenomena starting from macroscopic appearance of such evolution and to conserve the description within the framework of deterministic paradigm. In spite of the fact that we refuse to quantize hydromechanical variables in the sense of quantum theory and reject of y-functions for turbulence their place of the latter occupies the algebras of observable variables. Legitimating of their appearance is a decisive aspect of the suggested theory.