Skip to main content
SpringerLink
Log in

The growth and decay of weak discontinuities in relativistic fluids with vibrational relaxation

  • Published:
Acta Physica Academiae Scientiarum Hungaricae

Abstract

The propagation of weak discontinuities in relativistic fluids with vibrational relaxation has been studied. The velocity of propagation of a relativistic weak discontinuity has been determined. The fundamental equation governing the growth and decay of a relativistic weak wave has been obtained and solved. The relativistic results are shown to be in full agreement with earlier results of classical gasdynamics. The problem of breakdown of weak discontinuities has also been investigated. The critical timet c is determined when the breakdown of the wave will occur and consequently a shock wave will be formed due to non-linear steepening. It is shown that there exists a critical amplitude of the wave such that all compressive waves with an initial amplitude greater than the critical one will break down and a shock-type discontinuity will be formed, while an initial amplitude less than the critical one will result in a decay of the wave. The local and global behaviour of the wave amplitude is also discussed.

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. E. Becker, Areo. J.,74, 736, 1970.

    Google Scholar 

  2. R. M. Bowen andP. J. Chen, J. Math. Phys.,13, 958, 1972.

    Article  ADS  MathSciNet  Google Scholar 

  3. B. S. H. Rarity, J. Fluid Mech.,27, 49, 1967.

    Article  MATH  ADS  Google Scholar 

  4. C. Eckart, Phys. Rev.,58, 919, 1940.

    Article  MATH  ADS  Google Scholar 

  5. A. H. Taub, Phys. Rev.,74, 328, 1948.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  6. G. Saini, Proc. R. Soc.,A260, 61, 1961.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  7. N. Coburn, J. Math. Mech.,10, 361, 1961.

    MATH  MathSciNet  Google Scholar 

  8. R. P. Kanwal, J. Math. Mech.,15, 379, 1966.

    MATH  MathSciNet  Google Scholar 

  9. M. F. McCarthy, Int. J. Engng. Sci.,7, 209, 1969.

    Article  MATH  Google Scholar 

  10. R. Ram, Acta Phys. Hung.,44, 195, 1978.

    Article  Google Scholar 

  11. R. A. Grot andA. C. Eringen, Int. J. Engng. Sci.,4, 611, 1966.

    Article  Google Scholar 

  12. C. Trusedell andR. A. Toupin, The Classical Field Theories, in Handbuch der Physik,111/1 Springer, 1960.

  13. T. Y. Thomas, J. Math. Mech.,6, 311, 1957.

    MathSciNet  Google Scholar 

  14. T. Y. Thomas, Concepts from Tensor Analysis and Differential Geometry, 2nd edition, Academic Press, 1963.

  15. R. A. Grot, Int J. Engng. Sci.,6, 295, 1968.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Sciences, Institute of Technology, B.H.U., Varanasi, India

    Rishi Ram & H. N. Singh

Authors
  1. Rishi Ram
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. H. N. Singh
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ram, R., Singh, H.N. The growth and decay of weak discontinuities in relativistic fluids with vibrational relaxation. Acta Physica 46, 157–165 (1979). https://doi.org/10.1007/BF03159427

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03159427

Keywords

Search

Navigation