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# The Stationary Concentrated Vortex Model

1
Institute of Physics of the Earth, 10 B. Gruzinskaya, 123242 Moscow, Russia
2
Space Research Institute, 84/32 Profsouznaya Str., 117997 Moscow, Russia
3
Plasma Dynamics Group, Department of Automatic Control and Systems Engineering, University of Sheffield, Mappin 6 Str., Sheffield S1 3JD, UK
4
Space and Geophysical Laboratory, Applied Research Laboratory at the University of Texas (ARLUT), Austin, TX 78705, USA
5
Plasma Dynamics Group, School of Mathematics and Statistics, University of Sheffield, Hicks Building, Sheffield S3 7RH, UK
*
Author to whom correspondence should be addressed.
Climate 2021, 9(3), 39; https://doi.org/10.3390/cli9030039
Received: 25 January 2021 / Revised: 10 February 2021 / Accepted: 20 February 2021 / Published: 26 February 2021
A new model of an axially-symmetric stationary concentrated vortex for an inviscid incompressible flow is presented as an exact solution of the Euler equations. In this new model, the vortex is exponentially localised, not only in the radial direction, but also in height. This new model of stationary concentrated vortex arises when the radial flow, which concentrates vorticity in a narrow column around the axis of symmetry, is balanced by vortex advection along the symmetry axis. Unlike previous models, vortex velocity, vorticity and pressure are characterised not only by a characteristic vortex radius, but also by a characteristic vortex height. The vortex structure in the radial direction has two distinct regions defined by the internal and external parts: in the inner part the vortex flow is directed upward, and in the outer part it is downward. The vortex structure in the vertical direction can be divided into the bottom and top regions. At the bottom of the vortex the flow is centripetal and at the top it is centrifugal. Furthermore, at the top of the vortex the previously ascending fluid starts to descend. It is shown that this new model of a vortex is in good agreement with the results of field observations of dust vortices in the Earth’s atmosphere. View Full-Text
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MDPI and ACS Style

Onishchenko, O.; Fedun, V.; Horton, W.; Pokhotelov, O.; Astafieva, N.; Skirvin, S.J.; Verth, G. The Stationary Concentrated Vortex Model. Climate 2021, 9, 39. https://doi.org/10.3390/cli9030039

AMA Style

Onishchenko O, Fedun V, Horton W, Pokhotelov O, Astafieva N, Skirvin SJ, Verth G. The Stationary Concentrated Vortex Model. Climate. 2021; 9(3):39. https://doi.org/10.3390/cli9030039

Chicago/Turabian Style

Onishchenko, Oleg; Fedun, Viktor; Horton, Wendell; Pokhotelov, Oleg; Astafieva, Natalia; Skirvin, Samuel J.; Verth, Gary. 2021. "The Stationary Concentrated Vortex Model" Climate 9, no. 3: 39. https://doi.org/10.3390/cli9030039

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