On some mathematical model of turbulent flow with intensive self-mixing

This paper presents a new possibility of mathematical modeling of turbulent flow with intensive self-mixing. The flow is described in this model by a family of mappings ; , , t > t (o) such that, in general, does not imply The model allows a new approach to certain problems of turbulent flow. For example, there are possibilities to introduce some models of turbulent chemical reactors, or description of the unpredictable explosions of turbulence in the calm laminate flow. In this model we introduce mathematical tools that allow definition of various mixing states of the fluid. It is possible to formulate, in appropriate mathematical language, the idea that the given fluid can have various mixing states. It is also possible to determine the influence of a given mixing state on the flow parameters such as velocity field and density.