Skip to main content
SpringerLink
Log in

Theory of Vortex Rings

  • Chapter
  • First Online:
Book cover Paradoxes in Aerohydrodynamics

Part of the book series: Mathematical Engineering ((MATHENGIN))

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Lamb, G.: Gidrodinamika. M.-L.: GITTL, 928 s (1947)

    Google Scholar 

  2. Lavrentyev, M.A., Shabat, B.V.: Problemy gidrodinamiki i ih matematicheskiye modeli. 2 -ie izd. Moscow: Nauka, 408 s (1977)

    Google Scholar 

  3. Betchelor, Dzh.: Vvedeniye v dinamiku zhidkosti. Moscow: Mir. 758 s (1973)

    Google Scholar 

  4. Lugovtsov, B.A.: Turbulentnyie vyhrevyie kolcsa. Avtoref. dis. dokt. fiz.-mat. nauk. Novosibirsk, 40 s (1974)

    Google Scholar 

  5. Maxworthy, Т.: The structure and stability of vortex rings. Fluid Mech 51(I), 15–32 (1972)

    Google Scholar 

  6. Kriehel, A.R.: Vortex rings from underwater explosions. Pap. АSМЕ, № FE-36, pp. 12–17 (1972)

    Google Scholar 

  7. Riley, N.: Flows with concentrated vorticity: a report on EVROMECH 41. J. Fluid Mech. 62, 33–40 (1974)

    Article  MATH  Google Scholar 

  8. 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)

    Google Scholar 

  9. Windell, Sh.: Struktura i dinamika vihrevyh nitei. Sb. Vihrevyie dvizheniya zhidkosti. Moscow: Mir, S. 126–159 (1979)

    Google Scholar 

  10. 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)

    Google Scholar 

  11. Ahmetov, D.G., Kisarov, O.P.: Gidrodinamicheskaia struktura kolcsevogo vihria. Zhurnal prikl. meh. itehn. fiz., № 4, S. 120–123 (1966)

    Google Scholar 

  12. Buzukov, A.A.: Osobennosti obrazovaniya i dvizheniya kolcsevyh vihrei v vode. Zhurnal prikl. meh. iteh. fiz., №2, S. 153–160 (1971)

    Google Scholar 

  13. 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)

    Google Scholar 

  14. Lugovtsov, B.A.: O dvizhenii turbulentnogo vihrevogo kolcsa i perenose im passivnoi primesi. Vkn.: Nekotoryie problemy matematicheskoi mehaniki. Leningrad: Nauka (1970)

    Google Scholar 

  15. Tarasov, V.F.: Ocsenka nekotoryh parametrov turbulentnogo vihrevo gokolcsa. Vsb.: Din. sploshnoi sredy. Novosibirsk, vyp. 14, S. 120–127 (1973)

    Google Scholar 

  16. Tarasov, V.F.: Eksperimentalnyie issledovaniya turbulentnyh vihrevyh kolecs. Avtoref. dis. fiz.-mat.nauk. Novosibirsk, 20 s (1975)

    Google Scholar 

  17. 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)

    Google Scholar 

  18. Didden, N.: On the formation of vortex rings: rolling - up and production of circulation. Z Angew. Math. undPhysic. (ZAMP) 30(I), 101–116 (1979)

    Article  Google Scholar 

  19. Maxworthy, T.: Turbulent vortex rings. J. Fluid Mech. 64(2), 227–239 (1974)

    Article  MATH  Google Scholar 

  20. Maxworthy, T.: Some experimental studies of vortex rings. J. Fluid Mech. 81(3), 465–495 (1977)

    Article  Google Scholar 

  21. Oshima, G.: Motions of vortex rings in water. J. Phys. Soc. Jpn 32(4), 1125–1131 (1972)

    Article  Google Scholar 

  22. Sallet, D.: Impulsive motions of a circular disc with causes a vortex ring. Phys. Fluids 18(I), 109–111 (1975)

    Article  Google Scholar 

  23. 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.)

    Article  Google Scholar 

  24. Muller, Е., Didden, N.: ZurErzeugung der Zirculationbei der BildungeinesRingwirbels an einerDusenmundung. Strojnckycasopis 31(3), 363–373 (1980)

    Google Scholar 

  25. 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)

    Google Scholar 

  26. Pullin, D.: Vortex ring formation at tube and orifice openings. Phys. Fluids 22(3), 401–403 (1979)

    Article  MathSciNet  Google Scholar 

  27. Saffman, P.: On the formation of vortex rings. Stud. Appl. Math. 54(3), 261–268 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  28. 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)

    Google Scholar 

  29. Saffman, P.G.: The number of waves on unstable vortex rings. J. Fluid Mech. 84(4), 625–641 (1978)

    Article  MathSciNet  Google Scholar 

  30. Magarvey, R., Maclachy, C.: The formation and structure of vortex rings. Canad. J. Phys. 42(4), 678–683 (1964)

    Article  MATH  Google Scholar 

  31. Saffman, P.G.: The velocity of viscous vortex rings. Stud. Appl. Math. 49(4), 371–380 (1970)

    Article  MATH  Google Scholar 

  32. Kambe, T., Oshima, G.: Generation and decay of viscous vortex rings. J. Phys. Soc. Jpn 38(I), 271–280 (1975)

    Article  Google Scholar 

  33. Ditkin, V.A., Prudnikov, A.P.: Integralnyie preobrazovaniya i operacsionnoie ischisleniye. Nauka, Moscow (1974). 542 s

    Google Scholar 

  34. Sneddon, I.: Preobrazovaniye Furie. IL, 567 s (1955)

    Google Scholar 

  35. Kampe de Periert, I.: Harmonic analyses of the two-dimensional flow of an incompressible viscous fluid. Quart. Appl. Math. 6(I), 1–14 (1948)

    MathSciNet  Google Scholar 

  36. Shlihting, G.: Teoriya pogranichnogo sloia. Nauka, Moscow (1974). 710 s

    Google Scholar 

  37. Loicsianski, L.G.: Mehanika zhidkosti i gaza. Nauka, Moscow (1973). 846 s

    Google Scholar 

  38. Frosta, U., Mouldena, T.: Turbulentnost. Princsipy i primeneniye. Mir, Moscow (1980). 534 s

    Google Scholar 

  39. Klimontovich, I.A.: Statisticheskaia fizika. Nauka, Moscow (1982). 560 s

    Google Scholar 

  40. Govindaraju, S.P., Saffman, P.G.: Plow in a turbulant trailing vortex. Phys. Fluids 14(10), 2074–2080 (1971)

    Article  Google Scholar 

  41. Fercsiger, Dzh.: Chislennoiemodelirovaniyekrunyhvihreidliaraschetaturbulentnyhtecheniy. Raketnaiatehnikaikosmonavtika, №9: S. 56–67 (1977)

    Google Scholar 

  42. Eveling, W.: Discussion of the Klimontovich Theory of Hydrodynamic Turbulence. Annalen der Physik, 7 Folge, Band 40, Heft I, pp. 25–33, Leipzig (1983)

    Google Scholar 

  43. Yershin, Sh.A., Kaltaiev, A.: Obavtomodelnostirazvitiikolcsevogovihriavviazkoizhidkosti. Vsb.: Prikladnaiamehanika. Primeneniye matematicheskih metodov v yestestvoznanii, S. 50–55 (1979)

    Google Scholar 

  44. Kaltaiev, A.: Primeneniye metoda integralnyh preobrazovaniy k issledovaniyu koncsentrirovannyh vihrei. Avtoref. kand. fiz-mat nauk. Almaty (1984)

    Google Scholar 

  45. 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)

    Google Scholar 

  46. Berezovski, A., Kaplanski, F.: Vorticity distributions for thick and thin vortex pairs and rings. Arch. Mech. 47, 1015 (1995)

    MATH  Google Scholar 

  47. Kaplanski, F., Rudi, U.: Dynamics of a viscous vortex ring. Int. J. Fluid Mech. Res. 26, 618 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  48. Fukumoto, Y., Kaplanski, F.: Global time evolution of an axisymmetric vortex ring at low Reynolds numbers. Phys. Fluids 20, 053103 (2008)

    Article  MATH  Google Scholar 

  49. Ting, L.: Studies on the motion and decay of vortex filament. Lect. Notes Phys. 148, 67–105 (1981)

    Article  MATH  Google Scholar 

  50. Brasseur, J., Chang, I.-D.: Combination of kinematics with flow visualization to compute total circulation. AIAA J. 19, 878–884 (1981)

    Article  Google Scholar 

  51. Tung, C., Ting, L.: Motion and decay of vortex ring. Phys. Fluids 10(5), 901–910 (1967)

    Article  Google Scholar 

  52. 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)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Almaty, Kazakhstan

    Shakhbaz A. Yershin

Authors
  1. Shakhbaz A. Yershin
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing Switzerland

About this chapter

Cite this chapter

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

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-25673-3_13

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-25671-9

  • Online ISBN: 978-3-319-25673-3

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation