Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Some classes of two-dimensional vortex flows of an ideal fluid

  • 36 Accesses

  • 1 Citations

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

Literature cited

  1. 1.

    J. A. Shercliff, “Simple rotational flows,” J. Fluid Mech.,82, No. 4 (1977).

  2. 2.

    G. K. Batchelor, An Introduction to Fluid Dynamics, Cambridge Univ. Press (1973).

  3. 3.

    J. T. Stuart, “On finite-amplitude oscillations in laminar mixing layers,” J. Fluid Mech.,29, No. 3 (1967).

  4. 4.

    L. V. Ovsyannikov, Group Analysis of Differential Equations [in Russian], Nauka, Moscow (1978).

  5. 5.

    R. K. Bullough and P. J. Caudrey, Solitons, Springer-Verlag, Berlin (1980).

  6. 6.

    G. L. Lamb, Elements of Soliton Theory, Wiley-Interscience, New York (1980).

  7. 7.

    E. T. Whittaker and G. N. Watson, A Course of Modern Analysis, 4th Ed., Cambridge Univ. Press (1927).

  8. 8.

    A. I. Markushevich, The Remarkable Sines [in Russian], Nauka, Moscow (1974).

  9. 9.

    M. Kirsch, Differential Topology [Russian translation], Mir, Moscow (1979).

  10. 10.

    N. E. Zhukovskii, Vortex Theory of Propellers [in Russian], Gostekhizdat, Moscow (1950).

  11. 11.

    V. I. Arnol'd, “On an a priori estimate of the theory of hydrodynamic stability,” Izv. Vyssh. Uchebn. Saved., Mat., No. 5 (1966).

  12. 12.

    G. Bateman, MHD Instabilities [Russian translation], Energoizdat (1982).

  13. 13.

    Yu. B. Movsesyants, “Solitons in two-dimensional hydrodynamic models of a cold plasma,” Zh. Eksp. Teor. Fiz.,91, No. 2(8) (1986).

  14. 14.

    N. I. Yavorskii, “Exact solutions of the equation Δu=Sinh u,” Fluid Mechanics and Heat Transfer in One and Two-Phase Media [in Russian], Novosibirsk (1979).

  15. 15.

    E. B. Gledzer, F. V. Dolzhanskii, and A. M. Obukhov, Systems of the Hydrodynamic Type and their Applications [in Russian], Nauka, Moscow (1981).

Download references

Author information

Additional information

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 109–117, January–February, 1989.

The author thanks V. A. Vladirimov for detailed discussions of the results.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Kaptsov, O.V. Some classes of two-dimensional vortex flows of an ideal fluid. J Appl Mech Tech Phys 30, 105–112 (1989). https://doi.org/10.1007/BF00860713

Download citation

Keywords

  • Vortex
  • Mathematical Modeling
  • Mechanical Engineer
  • Industrial Mathematic
  • Ideal Fluid