On a new Lagrangian view on the evolution of vorticity in spatial flows

The purpose of the study is to extend to the spatial case proposed by G. B. Sizykh approach to a two-dimensional vorticity evolution, which is based on the idea of considering a vorticity evolution in the form of such a motion of vortex lines and tubes that the intensity of these tubes changes over time according to a predefined law. Method. Thorough analysis is determined by describing the flow velocity field of an ideal incompressible fluid and a viscous gas in the general case, using the idea of the movement of imaginary particles. Results. For any given time law of change of velocity circulation (i. e. for an exponential decay) of a real fluid along the contours the method of evaluating the field of velocity of such contours and vortex tubes is proposed (e. g. getting a field of imaginary particles, which transfer them). It is established that for a given time law the velocity of imaginary particles is determined ambiguously, and the method of how to adjust their motion preserving defined law of circulation change is proposed. Conclusion. A new Lagrangian approach to the evolution of vorticity in three-dimensional flows is derived, as well as the expressions for the contours' velocity, which imply stated changing over the time of the velocity circulation of a real fluid along any contour. This theoretical result can be utilized in spatial modifications of the viscous vortex domain method to limit the number of vector tubes used in calculations.