DOI: https://doi.org/10.20535/1810-0546.2017.4.102048

### Analytical Models Development of Compact Monopole Vortex Flows

#### Abstract

**Background. **Mathematical description of vortex flows as a part of basic fundamental concepts of continuum mechanics, hydro- and gas dynamics, thermal physics, theoretical basics of chemical engineering, geophysics, meteorology.

**Objective. **Replenishment of existing information in traditional scientific, technical and educational publications about vortices and their analytical models by new data for scientists, teachers, post-graduates and students with the purpose of using in further investigations of fluids and gas vortex motion.

**Methods. **Analytical review of existing vortex current models, including monopole compact vortices, on a basis of the latest data from scientific articles and specialized monographs and their comparison with traditional data containing in the known textbooks and educational materials.

**Results. **The lack of modern compact vortices models was revealed in traditional scientific, technical and educational literary sources. They include the compact analogs of the point vortex and Rankine vortex: quasi-point vortex and compact compensated vortex. On basis of these ones and similar to them solutions (circular vortex, vortex with triad constant vorticity zones) the models of compact helical flows and vortices with helical symmetry were elaborated. The solutions of such tasks were analyzed: diffusion of compact vortices (Taylor vortex, Kloosterziel solution), turbulent diffusion of compact vortex, solutions for quasi-compact (laminar and turbulent) vortex-source, vortex-sink and also solution of the problem about compact turbulent vortex generation by rotating cylinder. All considered models are consistent with the energy conservation law and have advantages in their use.

**Conclusions.**The article contains series of the latest analytical models that describe both laminar and turbulent dynamics of monopole vortex flows which have not been reflected in traditional publications up to the present. The further research must be directed to search of analytical models for the coherent vortical structures in flows of viscous fluids, particularly near curved surfaces, where known in hydromechanics “wall law” is disturbed and heat and mass transfer anomalies take place.

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