Abstract
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.
Similar content being viewed by others
References
Hayes W D, Self-similar strong shocks in an exponential medium,J. Fluid Mech. 32 (1968) 305–315
Grinfel’d M A, Ray method for calculating the wavefront intensity in nonlinear elastic material,PMM J. Appl. Math. Mech. 42 (1978) 958–977
Maslov V P, Propagation of shock waves in an isentropic non-viscous gas,J. Sov. Math. 13 (1980) 119–163
Prasad P, Extension of Huyghen’s construction of a wavefront to a nonlinear wavefront and a shockfront,Curr. Sci. 56 (1987) 50–54
Prasad P, Ravindran R and Sau A, On the characteristic rule for shocks,Appl. Math. Lett., (To appear)
Prasad P and Srinivasan R, On methods of calculating successive positions of a shock front,Acta Mech. 74 (1988) 81–93
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, 1985
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. 111
Srinivasan R and Prasad P, On the propagation of a multidimensional shock of arbitrary strength,Proc. Indian Acad. Sci. (Math. Sci.) 94 (1985) 27–42
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) 93–94
Whitham G B,Linear and Nonlinear Waves, (New York: John Wiley and Sons) 1974
Whitham G B, On shock dynamics,Proc. Indian Acad. Sci. (Math. Sci.) 96 (1987) 71–73
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Prasad, P. On shock dynamics. Proc. Indian Acad. Sci. (Math. Sci.) 100, 87–92 (1990). https://doi.org/10.1007/BF02881118
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02881118