On shock dynamics

  • Phoolan Prasad


This is in continuation of our paper On the propagation of a multi-dimensional shock of arbitrary strength’ published earlier in this journal (Srinivasan and Prasad [9]). We had shown in our paper that Whitham’s shock dynamics, based on intuitive arguments, cannot be relied on for flows other than those involving weak shocks and that too with uniform flow behind the shock. Whitham [12] refers to this as misinterpretation of his approximation and claims that his theory is not only correct but also provides a natural closure of the open system of the equations of Maslov [3]. The main aim of this note is to refute Whitham’s claim with the help of an example and a numerical integration of a problem in gasdynamics.


Shock propagation non-linear waves compressible flow 


  1. [1]
    Hayes W D, Self-similar strong shocks in an exponential medium,J. Fluid Mech. 32 (1968) 305–315CrossRefGoogle Scholar
  2. [2]
    Grinfel’d M A, Ray method for calculating the wavefront intensity in nonlinear elastic material,PMM J. Appl. Math. Mech. 42 (1978) 958–977MATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    Maslov V P, Propagation of shock waves in an isentropic non-viscous gas,J. Sov. Math. 13 (1980) 119–163CrossRefGoogle Scholar
  4. [4]
    Prasad P, Extension of Huyghen’s construction of a wavefront to a nonlinear wavefront and a shockfront,Curr. Sci. 56 (1987) 50–54Google Scholar
  5. [5]
    Prasad P, Ravindran R and Sau A, On the characteristic rule for shocks,Appl. Math. Lett., (To appear)Google Scholar
  6. [6]
    Prasad P and Srinivasan R, On methods of calculating successive positions of a shock front,Acta Mech. 74 (1988) 81–93MATHCrossRefMathSciNetGoogle Scholar
  7. [7]
    Ramanathan T M, Huyghen’s method of construction of weakly nonlinear wavefronts and shockfronts with application to hyperbolic caustic, Ph.D. Thesis, Indian Institute of Science, Bangalore, 1985Google Scholar
  8. [8]
    Ravindran R and Prasad P, Kinematics of a shockfront and resolution of a hyperbolic caustic, inAdvances in nonlinear waves (Ed) L Debnath, 1985, Pitman Research Notes in Mathematics, Vol II No. 111Google Scholar
  9. [9]
    Srinivasan R and Prasad P, On the propagation of a multidimensional shock of arbitrary strength,Proc. Indian Acad. Sci. (Math. Sci.) 94 (1985) 27–42MATHMathSciNetGoogle Scholar
  10. [10]
    Srinivasan R and Prasad P, Corrections to some expressions in “On the propagation of a multidimensional shock of arbitrary strength”,Proc. Indian Acad. Sci. (Math. Sci.) 100 (1990) 93–94MATHMathSciNetGoogle Scholar
  11. [11]
    Whitham G B,Linear and Nonlinear Waves, (New York: John Wiley and Sons) 1974MATHGoogle Scholar
  12. [12]
    Whitham G B, On shock dynamics,Proc. Indian Acad. Sci. (Math. Sci.) 96 (1987) 71–73CrossRefGoogle Scholar

Copyright information

© Indian Academy of Sciences 1990

Authors and Affiliations

  • Phoolan Prasad
    • 1
  1. 1.Department of Applied MathematicsIndian Institute of ScienceBangaloreIndia

Personalised recommendations