Skip to main content
Log in

Dynamics of Upward Jets with Newtonian Cooling

  • Statistical, Nonlinear, and Soft Matter Physics
  • Published:
Journal of Experimental and Theoretical Physics Aims and scope Submit manuscript

Abstract

The Rayleigh–Taylor instability which is responsible for the occurrence of narrow upward jets is studied in the scope of the nonhydrostatic model with horizontally nonuniform density and the Newtonian cooling. As analysis shows, the total hierarchy of instabilities in this model consists of three regimes—collapse, algebraic instability, and inertial motion. Realization of these stages, mutual transitions, and interference depend on a ratio between two characteristic time scales—collapse time and cooling time.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. G. Birkhoff, Hydrodynamics, a Study in Logic, Fact, and Similitude, 2nd Ed. (Princeton University Press, Princeton, 1960).

    MATH  Google Scholar 

  2. L. Rayleigh, Proc. London Math. Soc. 14, 170 (1883).

    MathSciNet  Google Scholar 

  3. V. P. Goncharov and V. I. Pavlov, JETP Lett. 96, 427 (2012).

    Article  ADS  Google Scholar 

  4. V. P. Goncharov and V. I. Pavlov, Phys. Rev. E 88, 023002 (2013).

    Article  ADS  Google Scholar 

  5. V. P. Goncharov and V. I. Pavlov, J. Exp. Theor. Phys. 117, 754 (2013).

    Article  ADS  Google Scholar 

  6. V. P. Goncharov and V. I. Pavlov, JETP Lett. 101, 438 (2015).

    Article  ADS  Google Scholar 

  7. V. P. Goncharov and V. I. Pavlov, Phys. Rev. E 91, 043004 (2015).

    Article  ADS  MathSciNet  Google Scholar 

  8. V. E. Zakharov and E. A. Kuznetsov, Phys. Usp. 55, 535 (2011).

    Article  ADS  Google Scholar 

  9. V. P. Goncharov and V. I. Pavlov, JETP Lett. 84, 384 (2006).

    Article  ADS  Google Scholar 

  10. V. P. Goncharov and V. I. Pavlov, Phys. Rev. E 76, 066314 (2007).

    Article  ADS  MathSciNet  Google Scholar 

  11. V. P. Goncharov, JETP Lett. 89, 393 (2009).

    Article  ADS  Google Scholar 

  12. V. P. Goncharov and V. I. Pavlov, J. Exp. Theor. Phys. 111, 124 (2010).

    Article  ADS  Google Scholar 

  13. V. P. Goncharov, J. Exp. Theor. Phys. 113, 714 (2011).

    Article  ADS  Google Scholar 

  14. V. P. Goncharov and V. I. Pavlov, Hamiltonian Vortex and Wave Dynamics (Geos, Moscow, 2008) [in Russian].

    Google Scholar 

  15. J. Eggers and M. A. Fontelos, Nonlinearity 22, R1 (2009).

    Article  Google Scholar 

  16. E. A. Kuznetsov, JETP Lett. 80, 83 (2004).

    Article  ADS  Google Scholar 

  17. E. A. Kuznetsov, V. Naulin, A. H. Nielsen, and J. J. Rasmussen, Phys. Fluids 19, 105110 (2007).

    Article  ADS  Google Scholar 

  18. V. P. Goncharov and V. I. Pavlov, JETP Lett. 90, 317 (2014).

    Article  ADS  Google Scholar 

  19. D. H. Peregrine, J. Fluid Mech. 27, 815 (1967).

    Article  ADS  Google Scholar 

  20. A. E. Green and P. M. Naghdi, J. Fluid Mech. 78, 237 (1976).

    Article  ADS  Google Scholar 

  21. T. Y. Wu, J. Eng. Mech. Div., Proc. ASCE 107, 501 (1981).

    Google Scholar 

  22. R. Camassa and D. D. Holm, Physica D 60, 1 (1992).

    Article  ADS  MathSciNet  Google Scholar 

  23. R. Camassa, D. D. Holm, and J. M. Hyman, Adv. Appl. Mech. 31, 1 (1994).

    Article  Google Scholar 

  24. E. Fermi, Collected Papers of Enrico Fermi (Univ. Chicago Press, Chicago, 1965), Vol. 2, Chap. 244, p. 816.

    Google Scholar 

  25. E. Fermi, Collected Papers of Enrico Fermi (Univ. Chicago Press, Chicago, 1965), Vol. 2, Chap. 245, p. 821.

    Google Scholar 

  26. S. Bowman, Math. Proc. Cambridge Phil. Soc. 102, 173 (1987).

    Article  ADS  Google Scholar 

  27. S. N. Vlasov, V. A. Petritshchev, and V. I. Talanov, Radiophys. Quantum Electron. 14, 1062 (1971).

    Article  ADS  Google Scholar 

  28. V. I. Talanov, JETP Lett. 11, 199 (1970).

    ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to V. P. Goncharov.

Additional information

Published in Russian in Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2018, Vol. 153, No. 2, pp. 329–338.

The article is published in the original.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Goncharov, V.P., Pavlov, V.I. Dynamics of Upward Jets with Newtonian Cooling. J. Exp. Theor. Phys. 126, 276–283 (2018). https://doi.org/10.1134/S106377611801003X

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S106377611801003X

Navigation