THE STABILITY OF PLANAR HYDRODYNAMIC SHOCK WAVES--A PILOT INVESTIGATION FOR THE MAGNETO-HYDRODYNAMIC SHOCK STABILITY PROBLEM. Chap.. 11 of THEORETICAL STUDY OF HYDROMAGNETIC STABILITY AND TURBULENCE. INVESTIGATIONS AND DETAILED RESULTS. Annual Report, Period: January 1-December 31, 1961
The stability of a planar hydrodynamic shock is investigated. The fluid on each side of the shock is taken to be an ideal fluid satisfying the adiabatic equation of state with a ratio of specific heats greater than unity. The standard non-relativistic shock conditions are used. In the unperturbed fluid state a frame of reference moving with the shock velocity is chosen. This can be accomplished because the system is Galilean invariant. The unperturbed flows are taken to be space and time independent so that the stability problem can be developed by means of a Fourier awlysis. By applying first-order perturbation theory to the linearized shock and fluid equations, a dispersion relation or consistency condition is derived which shows the plane hydrodynamic shock to be stable. The stability of planar shocks is not only the simplest and the most representative case which could be considered but is of direct significance for shocks of arbitrary geometry. Therefore, knowledge of the stability of planar shocks is useful in the analysis of shocks ihduced by an expanding bubble. This application of planar shock theory is valid because shocks respond in a purely local fashion to perturbations of wavelength small compared with the local radius of curvature and locally all shocks look planar. It is also noteworthy that a planar shock wave treated as a discontinuity has no characteristic length associated with it. Therefore, if planar shocks are found to be unstable, it will follow that those of any shape are also unstable at least with reference to small wavelength perturbations. (auth)
- Research Organization:
- Radio Corp. of America. Missile and Surface Radar Div., Moorestown, N.J.
- NSA Number:
- NSA-16-022721
- OSTI ID:
- 4812196
- Report Number(s):
- AFSWC-TDR-62-12(Vol.II)(Chap.1
- Resource Relation:
- Other Information: Orig. Receipt Date: 31-DEC-62
- Country of Publication:
- Country unknown/Code not available
- Language:
- English
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