Acta Mechanica

, Volume 74, Issue 1–4, pp 81–93 | Cite as

On methods of calculating successive positions of a shock front

  • P. Prasad
  • R. Srinivasan
Contributed Papers

Summary

In this paper we have discussed limits of the validity of Whitham's characteristic rule for finding successive positions of a shock in one space dimension. We start with an example for which the exact solution is known and show that the characteristic rule gives correct result only if the state behind the shock is uniform. Then we take the gas dynamic equations in two cases: one of a shock propagating through a stratified layer and other down a nonuniform tube and derive exact equations for the evolution of the shock amplitude along a shock path. These exact results are then compared with the results obtained by the characteristic rule. The characteristic rule not only incorrectly accounts for the deviation of the state behind the shock from a uniform state but also gives a coefficient in the equation which differ significantly from the exact coefficients for a wide range of values of the shock strength.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Maslov, V. P.: Propagation of shock waves in the isentropic nonviscous gas. J. Sov. Maths.13, 119–163 (1980).Google Scholar
  2. [2]
    Prasad, P.: Kinematics of a multi-dimensional shock of arbitrary strength in an ideal gas. Acta Mechanica45, 163–176 (1982).Google Scholar
  3. [3]
    Prasad, P.: Construction of a nonlinear wavefront and a shock front—an extension of Huyghen's method. Current Science56, 50–54 (1987).Google Scholar
  4. [4]
    Ramanathan, T. M., Prasad, P., Ravindran, R.: On the propagation of a weak shock front. Theory and Application, Acta Mechanica51, 167–177 (1984).Google Scholar
  5. [5]
    Ramanathan, T. M.: Huyghen's method of construction of weakly nonlinear fronts and shock fronts with application to hyperbolic caustic. Ph. D. Thesis, Indian Institute of Science, Bangalore (1985).Google Scholar
  6. [6]
    Ravindran, R., Prasad, P.: Kinematics of a shock front and resolution of a hyperbolic caustic. In: Advances in Nonlinear Waves Vol. II, (Debnath, L., ed.) 77–93, Pitman 1985.Google Scholar
  7. [7]
    Srinivasan, R., Prasad, P.: On the propagation of a multi dimensional shock of arbitrary strength. Proc. Indian Academy of Sciences49, 27–42 (1985).Google Scholar
  8. [8]
    Whitham, G. B.: Linear and nonlinear waves. New York: John Wiley—Interscience Monographs 1974.Google Scholar

Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • P. Prasad
    • 1
  • R. Srinivasan
    • 1
  1. 1.Department of Applied MathematicsIndian Institute of ScienceBangaloreIndia

Personalised recommendations