ON THE STRUCTURAL SIMILARITY OF STABLE FORMS OF SPIRAL-VORTEX MOTION

On the basis of the thermodynamic approach, inferences of the stability theory, and the method of dimensional analysis, we have obtained analytical dependences defi ning the relations between geometric sizes and rotation frequencies in three-dimensional spiral-vortex formations. To describe the vortex structure of the swirling fl ow of viscous and nonviscous fl uids, we propose to introduce into consideration the notion the order parameter. It has been shown that helicity as a characteristic of the measure of decrease in the symmetry of a moving medium connected with its order is not only an invariant of the vortex fl ow of nonviscous media, but can also be used as the order parameter for describing the geometrical similarity of spiral-vortex structures in real fl uids.
   
Author:  O. V. Mitrofanova
Keywords:  vortex structures, helicity, screw motion, stability, invariance
Page:  1119