Abstract
The actual motion of liquid and gas, with rare exceptions, always has a vortex structure. Therefore, vortex flows are the subject of numerous studies, both of a theoretical and an experimental nature. From all the varieties of vortex motion of a viscous fluid, the so-called circular vortex aroused particular interest. The latter is often observed in nature due to some random or special perturbations and can be easily artificially reproduced through fairly simple means, even at home. This apparent simplicity generates a passionate interest in the phenomenon among the specialists in various fields due to the comparative availability of observations on the one hand and the realization of unusualness of the phenomena on the other. Back in the late nineteenth century, physicists tried to create on its basis a vortex model of the atom [1–3]. Engineering thought has always strived for opportunities hidden in it of useful application for the benefit of mankind [4–10]. For fluid mechanics, it is some kind of “touchstone” for testing the continually evolving methods of theoretical hydrodynamics and consolidation of its achievements. A flow generated by a concentrated vortex ring was studied nearly at every stage of its development, but nevertheless the problem still hasn’t obtained a satisfactory solution with sufficient completeness which is consistent with the experiment.
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References
Lamb, G.: Gidrodinamika. M.-L.: GITTL, 928 s (1947)
Lavrentyev, M.A., Shabat, B.V.: Problemy gidrodinamiki i ih matematicheskiye modeli. 2 -ie izd. Moscow: Nauka, 408 s (1977)
Betchelor, Dzh.: Vvedeniye v dinamiku zhidkosti. Moscow: Mir. 758 s (1973)
Lugovtsov, B.A.: Turbulentnyie vyhrevyie kolcsa. Avtoref. dis. dokt. fiz.-mat. nauk. Novosibirsk, 40 s (1974)
Maxworthy, Т.: The structure and stability of vortex rings. Fluid Mech 51(I), 15–32 (1972)
Kriehel, A.R.: Vortex rings from underwater explosions. Pap. АSМЕ, № FE-36, pp. 12–17 (1972)
Riley, N.: Flows with concentrated vorticity: a report on EVROMECH 41. J. Fluid Mech. 62, 33–40 (1974)
Kricskiy, V.S., Loktev, B.I., Maliar, A.M., Onushkin, I.P.: Issledovaniye nekotoryh osobennostei aerodinamiki vinta na perehodnyh rezhimah poleta vertolieta. Vkn.: Aviacsiya i vozduhovlavaniye. Moscow: Nauka, S. 16–21 (1981)
Windell, Sh.: Struktura i dinamika vihrevyh nitei. Sb. Vihrevyie dvizheniya zhidkosti. Moscow: Mir, S. 126–159 (1979)
Marchenko, A.V., Kartavcsev, S.V.: Osobennosti aerodinamiki gazogorelochnyh ustroistv s vyhrevymi kolcsami. Sb.: Teplotehn. procsessov vyplavki stali i splavov. Sverdlovsk, №6, S. 18–20 (1979)
Ahmetov, D.G., Kisarov, O.P.: Gidrodinamicheskaia struktura kolcsevogo vihria. Zhurnal prikl. meh. itehn. fiz., № 4, S. 120–123 (1966)
Buzukov, A.A.: Osobennosti obrazovaniya i dvizheniya kolcsevyh vihrei v vode. Zhurnal prikl. meh. iteh. fiz., №2, S. 153–160 (1971)
Lugovtsov, B.A., Lugovtsov, A.A., Tarasov, V.F.: O dvizhenii turbulentnogo vihrevogo kolcsa. V sb.: Din. sploshnoi sredy. Novosibirsk, vyp. 3, S. 50–60 (1969)
Lugovtsov, B.A.: O dvizhenii turbulentnogo vihrevogo kolcsa i perenose im passivnoi primesi. Vkn.: Nekotoryie problemy matematicheskoi mehaniki. Leningrad: Nauka (1970)
Tarasov, V.F.: Ocsenka nekotoryh parametrov turbulentnogo vihrevo gokolcsa. Vsb.: Din. sploshnoi sredy. Novosibirsk, vyp. 14, S. 120–127 (1973)
Tarasov, V.F.: Eksperimentalnyie issledovaniya turbulentnyh vihrevyh kolecs. Avtoref. dis. fiz.-mat.nauk. Novosibirsk, 20 s (1975)
Vladimirov, V.A., Tarasov, F.V.: K formirovaniyu vihrevyh kolecs pri bolshih chislah Reinoldsa. Vsb.: Din. sploshnoi sredy. Novosibirsk, vyp. 43, S. 54–156 (1979)
Didden, N.: On the formation of vortex rings: rolling - up and production of circulation. Z Angew. Math. undPhysic. (ZAMP) 30(I), 101–116 (1979)
Maxworthy, T.: Turbulent vortex rings. J. Fluid Mech. 64(2), 227–239 (1974)
Maxworthy, T.: Some experimental studies of vortex rings. J. Fluid Mech. 81(3), 465–495 (1977)
Oshima, G.: Motions of vortex rings in water. J. Phys. Soc. Jpn 32(4), 1125–1131 (1972)
Sallet, D.: Impulsive motions of a circular disc with causes a vortex ring. Phys. Fluids 18(I), 109–111 (1975)
Sullivan, I., Widnall, S., Ezekiel, S.: A study of vortex rings using a laser Dappler velocimeter. AIAA J. II, 1384–1389 (1973) (Imeietsya perevod: Raketnaia tehnika i kosmonavtika. 1973, T. II, №10, S. 31–36.)
Muller, Е., Didden, N.: ZurErzeugung der Zirculationbei der BildungeinesRingwirbels an einerDusenmundung. Strojnckycasopis 31(3), 363–373 (1980)
Liess, C., Didden, N.: Experimente rum Einflus der Anfangsbeding-ungen auf die Instabilitat von Ringwirbeln. Z. Angew. Math. Mech. (ZAMM) 56(3), T206–T208 (1976)
Pullin, D.: Vortex ring formation at tube and orifice openings. Phys. Fluids 22(3), 401–403 (1979)
Saffman, P.: On the formation of vortex rings. Stud. Appl. Math. 54(3), 261–268 (1975)
Ogava, S., Igarashi, M.: Behaviours of the vortex ring in the domain of the high-Reynolds number. J. Coll. Eng. Nihon Univ. A20, 97–113 (1979)
Saffman, P.G.: The number of waves on unstable vortex rings. J. Fluid Mech. 84(4), 625–641 (1978)
Magarvey, R., Maclachy, C.: The formation and structure of vortex rings. Canad. J. Phys. 42(4), 678–683 (1964)
Saffman, P.G.: The velocity of viscous vortex rings. Stud. Appl. Math. 49(4), 371–380 (1970)
Kambe, T., Oshima, G.: Generation and decay of viscous vortex rings. J. Phys. Soc. Jpn 38(I), 271–280 (1975)
Ditkin, V.A., Prudnikov, A.P.: Integralnyie preobrazovaniya i operacsionnoie ischisleniye. Nauka, Moscow (1974). 542 s
Sneddon, I.: Preobrazovaniye Furie. IL, 567 s (1955)
Kampe de Periert, I.: Harmonic analyses of the two-dimensional flow of an incompressible viscous fluid. Quart. Appl. Math. 6(I), 1–14 (1948)
Shlihting, G.: Teoriya pogranichnogo sloia. Nauka, Moscow (1974). 710 s
Loicsianski, L.G.: Mehanika zhidkosti i gaza. Nauka, Moscow (1973). 846 s
Frosta, U., Mouldena, T.: Turbulentnost. Princsipy i primeneniye. Mir, Moscow (1980). 534 s
Klimontovich, I.A.: Statisticheskaia fizika. Nauka, Moscow (1982). 560 s
Govindaraju, S.P., Saffman, P.G.: Plow in a turbulant trailing vortex. Phys. Fluids 14(10), 2074–2080 (1971)
Fercsiger, Dzh.: Chislennoiemodelirovaniyekrunyhvihreidliaraschetaturbulentnyhtecheniy. Raketnaiatehnikaikosmonavtika, №9: S. 56–67 (1977)
Eveling, W.: Discussion of the Klimontovich Theory of Hydrodynamic Turbulence. Annalen der Physik, 7 Folge, Band 40, Heft I, pp. 25–33, Leipzig (1983)
Yershin, Sh.A., Kaltaiev, A.: Obavtomodelnostirazvitiikolcsevogovihriavviazkoizhidkosti. Vsb.: Prikladnaiamehanika. Primeneniye matematicheskih metodov v yestestvoznanii, S. 50–55 (1979)
Kaltaiev, A.: Primeneniye metoda integralnyh preobrazovaniy k issledovaniyu koncsentrirovannyh vihrei. Avtoref. kand. fiz-mat nauk. Almaty (1984)
Kaltaiev, A., Yershin, Sh.A.: Primeneniye metoda integralnyh preobrazovaniy k issledovaniyu koncsentrirovannyh vihrei. Materialy Vsesoiuznogo nauchnogo soveshaniya po teoreticheskim i prikladnym aspektam turbulentnyh techeniy, ch. 1. Tallin (1985)
Berezovski, A., Kaplanski, F.: Vorticity distributions for thick and thin vortex pairs and rings. Arch. Mech. 47, 1015 (1995)
Kaplanski, F., Rudi, U.: Dynamics of a viscous vortex ring. Int. J. Fluid Mech. Res. 26, 618 (1999)
Fukumoto, Y., Kaplanski, F.: Global time evolution of an axisymmetric vortex ring at low Reynolds numbers. Phys. Fluids 20, 053103 (2008)
Ting, L.: Studies on the motion and decay of vortex filament. Lect. Notes Phys. 148, 67–105 (1981)
Brasseur, J., Chang, I.-D.: Combination of kinematics with flow visualization to compute total circulation. AIAA J. 19, 878–884 (1981)
Tung, C., Ting, L.: Motion and decay of vortex ring. Phys. Fluids 10(5), 901–910 (1967)
Yershin, Sh.A., Kaltaiev, A.: Ob avtomodel’nosty razvitiya kol’cevogo vihrya v vyazkoy jidkosty. V sb.: Prikladnaya mehanika. Primenenye matematicheskih metodov v estestvoznanii, S. 50–55 (1979)
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Yershin, S.A. (2017). Theory of Vortex Rings. In: Paradoxes in Aerohydrodynamics. Mathematical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-25673-3_13
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