Modelling of turbulent regimes changes

A.M.Mukhamedov

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

Tatarstan 9-15, Kazan 420021, RUSSIA

e-mail: Rashidma@mail.ru

 

Given paper is the development of the previous papers by the same author "Turbulence as a strange attractor of multimode evolution" and "On the mechanism of mode interactions". It reveals a new point of view for changing processes of turbulent regimes. In analogy with laminar case, it claims that turbulent regimes and their changing must be described by evolution mechanism presented by balance equations of all excited modes. Thereby the paradigm of classical hydromechanical description extends into turbulent mechanic. As a consequence it becomes clear the distinction between changing of regimes that lead to changing of the number of freedom degrees from the one that entail only of bifurcation's of characteristics of motion. Bifurcation's that do not change the number of freedom degrees belong to domain of bifurcation theory. These aspects are nontrivial if chaotic attractor is not rough, as, for example, it is for Lorenz's attractor.љ The paper deals with the others.

The main feature of our model consists in the two-level organization of interaction mechanism. Its structure consist of two substructures: 1) nonspecific level of influence of relaxing modes that reveal interactions of them with unstable modes, and 2) specific level of interactions between unstable modes in themselves. The first is due to external surround actions, assumed stationary. The second defined by balance equations of excited modes. Such structure provides the transitions of turbulent modes from one level of mode interactions to another. Hence, these transitions are strongly controlled by proper balance equations. Its features are of interest for given paper.

As an example of introducing of new modes that raise the number of them we offer modes of vortex that consider as independent from velocity. Balance equations of these modes come from asymmetrical hydromechanic. We put them on constructing of interaction mechanism between velocity modes and additional vortex modes. In more detail, we consider the changing of 3-modes regime represented by velocity's pulsation only, into 4-modes regime which additional mode controlled by balance equation of variable of extensive type. In this case, we give an example of regime changing. For instance, the transition from Lorenz's attractor to Rossler's one is shown. For intermediate regime, the influence of additional mode on bifurcation's of chaotic dynamic investigated for the case of Lorenz's dynamic.