Skip to main content
SpringerLink
Log in

Vorticity evolution in liquids and gases

  • Published:
Fluid Dynamics Aims and scope Submit manuscript

Abstract

It is proved that in any vortex flow of a liquid or a gas the vorticity evolution can be considered as the displacement of vortex tubes at a certain velocity U which generally is not the same as the fluid velocity. For a viscous incompressible fluid a technique of calculating U from the fluid velocity field is proposed.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. N.E. Kochin, I.A. Kibel’, and I.V. Roze, Theoretical Hydromechanics. Vol. 1 [in Russian], Fizmatgiz, Moscow (1963).

    Google Scholar 

  2. V.N. Golubkin and G.B. Sizykh, “Some General Properties of Plane-Parallel Viscous Flows,” Fluid Dynamics 22(3), 479 (1987).

    Article  ADS  Google Scholar 

  3. M.A. Brutyan, V.N. Golubkin, and P.L. Krapivskii, “On the Bernoulli Equation for Axisymmetric Viscous Flows,” Uch. Zap. TsAGI 19(2), 98 (1988).

    Google Scholar 

  4. L. Rosenhead, “The Formation of Vortices from a Surface of Discontinuity,” Proc. Roy. Soc. London. Ser. A 134,170 (1931).

    Article  ADS  Google Scholar 

  5. S.M. Belotserkovskii and M.I. Nisht, Separated and Separationless Ideal-Fluid Flows past Thin Wings [in Russian], Nauka, Moscow (1978).

    Google Scholar 

  6. G.-H. Cottet and P. Koumoutsakos, Vortex Methods: Theory and Practice, Cambridge Univ. Press, Cambridge (2000).

    Book  Google Scholar 

  7. V.A. Gutnikov, I.K. Lifanov, and A.V. Setukha, “Simulation of the Aerodynamics of Buildings and Structures by Means of the Closed Vortex Loop Method,” Fluid Dynamics 41(4), 555 (2006).

    Article  ADS  MATH  Google Scholar 

  8. G.Ya. Dynnikova, “The Lagrangian Approach to the Solution of the Time-Dependent Navier-Stokes Equations,” Dokl. Ross. Akad. Nauk 399, 42 (2004).

    MathSciNet  Google Scholar 

  9. L.G. Loitsyanskii, Mechanics of Liquids and Gases, Pergamon Press, Oxford (1966).

    Google Scholar 

  10. G.K. Batchelor, Introduction to Fluid Dynamics, Cambridge Univ. Press, Cambridge (1967).

    MATH  Google Scholar 

  11. G.Ya. Dynnikova, “The Integral Formula for Pressure Field in the Nonstationary Barotropic Flows of Viscous Fluid,” J. Math. Fluid Mech. 16, 145 (2014).

    Article  ADS  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Steklov Mathematical Institute, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991, Russia

    V. V. Markov

  2. Moscow Institute of Physics and Technology (State University), Institutskii per. 9, Dolgoprudnyi Moscow oblast, 141700, Russia

    G. B. Sizykh

Authors
  1. V. V. Markov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. B. Sizykh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. V. Markov.

Additional information

Original Russian Text © V.V. Markov, G.B. Sizykh, 2015, published in Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, 2015, Vol. 50, No. 2, pp. 8–15.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Markov, V.V., Sizykh, G.B. Vorticity evolution in liquids and gases. Fluid Dyn 50, 186–192 (2015). https://doi.org/10.1134/S0015462815020027

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0015462815020027

Keywords

Search

Navigation