On methods of calculating successive positions of a shock front
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
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.
- Maslov, V. P.: Propagation of shock waves in the isentropic nonviscous gas. J. Sov. Maths.13, 119–163 (1980).
- Prasad, P.: Kinematics of a multi-dimensional shock of arbitrary strength in an ideal gas. Acta Mechanica45, 163–176 (1982).
- Prasad, P.: Construction of a nonlinear wavefront and a shock front—an extension of Huyghen's method. Current Science56, 50–54 (1987).
- Ramanathan, T. M., Prasad, P., Ravindran, R.: On the propagation of a weak shock front. Theory and Application, Acta Mechanica51, 167–177 (1984).
- 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).
- 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.
- Srinivasan, R., Prasad, P.: On the propagation of a multi dimensional shock of arbitrary strength. Proc. Indian Academy of Sciences49, 27–42 (1985).
- Whitham, G. B.: Linear and nonlinear waves. New York: John Wiley—Interscience Monographs 1974.
- On methods of calculating successive positions of a shock front
Volume 74, Issue 1-4 , pp 81-93
- Cover Date
- Print ISSN
- Online ISSN
- Additional Links
- Industry Sectors