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Spherical Shock Waves: The Self-Similar Solution

  • Seán Prunty
Chapter
Part of the Shock Wave and High Pressure Phenomena book series (SHOCKWAVE)

Abstract

This particular chapter has an independent character and deals almost exclusively with Taylor’s analysis of very strong spherical shocks. The presentation follows Taylor’s analysis and notation in relation to the similarity solution for the point source explosion in air. Following his analysis, the partial differential equations in Eulerian form are reduced to a set of coupled ordinary differential equations which are numerically integrated. Taylor’s analytical approximations for the pressure, density and velocity are presented and these turn out to be remarkably accurate when compared to the numerical solutions. His analysis of the energy left in the atmosphere after the blast wave has propagated away has also been presented and discussed. The chapter concludes with an approximate treatment of very strong shock, which is based on the particular nature of the point source solution where most of the material is piled up at the shock front.

Keywords

Point source solution Self-similar solution Spherical shock waves Taylor’s analysis of very strong shocks Wasted energy Approximate treatment of strong shocks 

References

  1. 1.
    R. Serber, The Los Alamos Primer: The First Lectures on How to Build an Atomic Bomb (University of California Press, Berkeley, CA, 1992)Google Scholar
  2. 2.
    B. Cameron Reed, The Physics of the Manhattan Project, 3rd edn. (Springer, Heidelberg, 2015)zbMATHGoogle Scholar
  3. 3.
    J.D. Logan, Applied Mathematics; A Contemporary Approach (John Wiley & Sons, Inc., New York, 1987), Chapter 7zbMATHGoogle Scholar
  4. 4.
    G.I. Taylor, The formation of a blast wave by a very intense explosion, I. Theoretical discussion. Proc. Royal Soc. A 201, 159 (1950)CrossRefGoogle Scholar
  5. 5.
    J. von Neumann, The point source solution, in Collected Works, vol. VI, (Pergamon Press, New York, 1976), p. 219Google Scholar
  6. 6.
    H.A. Bethe et al., LA-2000 Report (Los Alamos Scientific Laboratory of the University of California, Los Alamos, New Mexico, 1958)Google Scholar
  7. 7.
    L.I. Sedov, Similarity and Dimensional Methods in Mechanics (Academic Press, New York/London, 1959)zbMATHGoogle Scholar
  8. 8.
    L.D. Landau, E.M. Lifshitz, Fluid Mechanics (Pergamon Press, London, 1966). Chapter 9Google Scholar
  9. 9.
    R.E. Scraton, Basic Numerical Methods (Edward Arnold Pub. Ltd., London, 1984)zbMATHGoogle Scholar
  10. 10.
    H. Bethe, J. Hirschfelder, V. Waters, LA-213 Report (Los Alamos Scientific Laboratory of the University of California, Los Alamos, New Mexico, 1946)Google Scholar
  11. 11.
    G.I. Taylor, The formation of a blast wave by a very intense explosion, II. The atomic explosion of 1945. Proc. Royal Soc., A 201, 175 (1950)CrossRefGoogle Scholar
  12. 12.
    G.G. Chernyi, The problem of a point explosion. Dokl. Akad. Nauk SSSR 112, 213 (1957)MathSciNetGoogle Scholar
  13. 13.
    Y.B. Zel’dovich, Y.P. Raizer, Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena (Dover Publications Inc., Mineola, New York, 2002), Section 26Google Scholar
  14. 14.
    C.E. Needham, Blast Waves (Springer, Berlin, Heidelberg, 2010), Section 4.2CrossRefGoogle Scholar
  15. 15.
    J.L. Taylor, An exact solution of the spherical blast wave problem. Phil. Mag. 46, 317 (1955)MathSciNetCrossRefGoogle Scholar
  16. 16.
    P.L. Sachdev, Shock Waves and Explosions (Chapman & Hall, London, 2004), Chapter 3CrossRefGoogle Scholar
  17. 17.
    J.H.S. Lee, The Gas Dynamics of Explosions (Cambridge University Press, New York, 2016), Chapter 4CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Seán Prunty
    • 1
  1. 1.BallincolligIreland

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