фХТВХМЕОФОПУФШ ЛБЛ УФТБООЩК БФФТБЛФПТ

НОПЗПНПДПЧПК ЬЧПМАГЙЙ

б.н.нХИБНЕДПЧ

лзфх ЙН. б.о.фХРПМЕЧБ

фБФБТУФБО, 9-15, лБЪБОШ 420021, тпууйс

e-mail: Rashidma@mail.ru

 

This paper deals with fundamental properties of turbulent motion. Undoubtedly that specific character of turbulence consists in the loss of individuality turbulent formations during their evolution. Nevertheless, this feature still does not have an adequate description in the formalism of existing models. Given paper construct required behavior by introducing new turbulent mixing mechanism. For developed turbulent motion, such mechanism is redused to ensemble of turbulent trajectories that present evolution of hydromechanical variables.

The description uses multimode princnple that represents hydromechanical variables of the steady turbulent flow as finite sums, named modes. For instance, velocity distribution presents by

                                                    (1)

where х – physical space coordinates, y – vector mode amplitude,  - covectors that perform vector of mode amplitudes into physically observable quantity. Representation (1) defines hydromechanical variables as fields of vector bundle, with base given by physical space and fibre presented by the values of mode amplitudes. This bundle becomes phase space of turbulent evolution. Projection of marked above trajectories into base creates visible picture of turbulence.

            Equations of mode amplitude evolution defined by Pfaff’s system

                                     (2)

Objects  and define connection and vertical vector field of phase space respectively. System (2) implied non-complete integrable. A set of all one-dimensional integral varieties of this system is considered as an ensemble of turbulent trajectories. Along these trajectories, mode evolution is completely defined by initial data. Substitution of a concrete trajectory in (1) will define development of the appropriate hydromechanical variable only along chosen base curve. Hence, evolution of all hydromechanical variables will be divided into layers.

Non-integrability of (2) and non-zero curvature of bundles connection are interpreted as a spatial heterogeneity of turbulent regimes.  The number of modes presented the number of freedom degrees of turbulent regime together with marked above objects defines the turbulent structure. Example of such structure with three freedom degrees that average flow presented by the simple shift and pulsation’s of Lorenz’s attractor type is constructed.