Vortex rings: history and state of the art
1
Shevchenko Kiev National University, Kiev, Ukraine
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2
“KPI” National Technical University of Ukraine, Kiev, Ukraine
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3
Institute of Hydromechanics, Ukrainian National Academy of Sciences, Kiev, Ukraine
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Publication type: Journal Article
Publication date: 2012-11-18
scimago Q3
SJR: 0.280
CiteScore: 0.7
Impact factor: —
ISSN: 10723374, 15738795
General Mathematics
Statistics and Probability
Applied Mathematics
Abstract
In the present paper, we describe the fascinating 150-year history of vortex dynamics, which started from the classical work by H. Helmholtz (1858). This work contains not only the general theorems on vortex motion, but also a special section devoted to axisymmetric circular vortex filaments and, in particular, to vortex rings. The aim of our investigation is both to clarify some purely mathematical questions connected with the Dyson model for coaxial vortex rings with a small circular cross-section in an ideal incompressible fluid and to provide a historical overview of the achievements in experimental, analytical, and numerical studies of the interaction of vortex rings. The model is illustrated by several examples of the motion of vortex rings. Finally, we present a complete classification of the interactions of two coaxial vortex rings in an ideal fluid.
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Meleshko V. V., Gourjii A. A., Krasnopolskaya T. Vortex rings: history and state of the art // Journal of Mathematical Sciences. 2012. Vol. 187. No. 6. pp. 772-808.
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Meleshko V. V., Gourjii A. A., Krasnopolskaya T. Vortex rings: history and state of the art // Journal of Mathematical Sciences. 2012. Vol. 187. No. 6. pp. 772-808.
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RIS
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TY - JOUR
DO - 10.1007/s10958-012-1100-0
UR - https://doi.org/10.1007/s10958-012-1100-0
TI - Vortex rings: history and state of the art
T2 - Journal of Mathematical Sciences
AU - Meleshko, V. V.
AU - Gourjii, A A
AU - Krasnopolskaya, T.S.
PY - 2012
DA - 2012/11/18
PB - Springer Nature
SP - 772-808
IS - 6
VL - 187
SN - 1072-3374
SN - 1573-8795
ER -
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BibTex (up to 50 authors)
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@article{2012_Meleshko,
author = {V. V. Meleshko and A A Gourjii and T.S. Krasnopolskaya},
title = {Vortex rings: history and state of the art},
journal = {Journal of Mathematical Sciences},
year = {2012},
volume = {187},
publisher = {Springer Nature},
month = {nov},
url = {https://doi.org/10.1007/s10958-012-1100-0},
number = {6},
pages = {772--808},
doi = {10.1007/s10958-012-1100-0}
}
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MLA
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Meleshko, V. V., et al. “Vortex rings: history and state of the art.” Journal of Mathematical Sciences, vol. 187, no. 6, Nov. 2012, pp. 772-808. https://doi.org/10.1007/s10958-012-1100-0.