Abstract
The maximum path L MAX of vortex rings (toroidal vortices) in air and water before the beginning of their decay was experimentally determined in a wide variation range of their initial integral characteristics. A formula for L MAX was derived as a function of primary characteristics of such vortices from the laws of their motion and energy variation. It was shown that this formula is in satisfactory agreement with experimental data.
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References
O. Reynolds, Nature 14, 477 (1876).
R. Wood, Nature 63, 418 (1901).
N. E. Zhukovskii, Note about Motion of Vortex Rings (Moscow University, Moscow, 1907) [in Russian].
R. H. Magarvey and C. S. Maclatcky, Canad. J. Phys. 42, 678 (1964).
B. A. Lugovtsov, Doctoral Dissertation in Mathematics and Physics (Institute of Hydrodynamics, Siberian Branch of the Academy of Sciences of the USSR, Novosibirsk, 1973).
M. A. Lavrent’ev and B.V. Shabat, Problems of Hydrodynamics and their Mathematical Models (Nauka, Moscow, 1973) [in Russian].
J. P. Sullivan, S. E. Windall, and S. Ezekiel, AIAA J. 11, 1384 (1973).
V. F. Tarasov, Candidate’s Dissertation in Mathematics and Physics (Institute of Hydrodynamics, Siberian Branch of the Academy of Sciences of the USSR, Novosibirsk, 1975).
T. Maxworthy, J. Fluid Mech. 81, 465 (1977).
K. Shariff and M. Leonard, Ann. Rev. FluidMech. 24, 235 (1992).
V. I. Boyarintsev, T. E. Boyarintseva, D. G. Korotaev, et al., Izv. RAN. Ser.MZhG, No. 3, 125 (1997).
M. Gharib, E. Rambod, and K. Shariff, J. FluidMech. 360, 121 (1998).
T. E. Faber, Fluid Dynamics for Physicists (Univ. press, Cambridge, 2001).
P. G. Saffman, Vortex dynamics (Univ. press, Cambridge, 1992).
D. G. Akhmetov, Candidate’s Dissertation in Mathematics and Physics (Institute of Hydrodynamics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, 2002).
S. V. Alekseenko, P. A. Kuibin, and V. L. Okulov, Introduction to the Theory of Concentrated Vortices (ITF SO RAN, Novosibirsk, 2003) [in Russian].
D. G. Akhmetov, Vortex Rings (Akadem. Izd. “Geo”, Novosibirsk, 2007) [in Russian].
U. Yusupaliev, Fiz. Plazmy 31, 543 (2005) [Plasma Phys. Rep. 31, 497 (2005)].
U. Yusupaliev, Kratkie Soobshcheniya po Fizike FIAN, No. 10, 39 (2004) [Bulletin of the Lebedev Physics Institute, No. 10, 32 (2004)].
U. Yusupaliev, Candidate’s Dissertation in Mathematics and Physics (MGU, Moscow, 1988).
A. F. Aleksandrov, V. A. Chernikov, and U. Yusupaliev, Teplofiz. Vysok. Temp. 26, 639 (1988).
U. Yusupaliev, Kratkie Soobshcheniya po Fizike FIAN, No. 6, 46 (2005) [Bulletin of the Lebedev Physics Institute, No. 6, 37 (2005)].
U. Yusupaliev, P. U. Yusupaliev, and S. A. Shuteev, Kratkie Soobshcheniya po Fizike FIAN, No. 5, 41 (2006) [Bulletin of the Lebedev Physics Institute, No. 5, 34 (2006)].
U. Yusupaliev, P. U. Yusupaliev, and S. A. Shuteev, Zh. Tekh. Fiz. 77(7), 50 (2007) [Tech. Phys. 52, 872 (2007)].
U. Yusupaliev, P. U. Yusupaliev, and S. A. Shuteev, Fiz. Plazmy 33, 226 (2007) [Plasma Phys. Rep. 33, 198 (2007)].
U. Yusupaliev, S. A. Shuteev, P. U. Yusupaliev, and V. V. Chubarov, Kratkie Soobshcheniya po Fizike FIAN 35(11), 45 (2008) [Bulletin of the Lebedev Physics Institute 35, 344 (2008)].
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Original Russian Text © U. Yusupaliev, S.A. Shuteev, E.E. Vinke, P.U. Yusupaliev, 2010, published in Kratkie Soobshcheniya po Fizike, 2010, Vol. 37, No. 8, pp. 3–13.
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Yusupaliev, U., Shuteev, S.A., Vinke, E.E. et al. Vortex rings and plasma toroidal vortices in a homogeneous infinite medium. I. Maximum vortex path. Bull. Lebedev Phys. Inst. 37, 227–233 (2010). https://doi.org/10.3103/S1068335610080014
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DOI: https://doi.org/10.3103/S1068335610080014