The theory of shock-wave stability
Abstract
The stability of shock waves is investigated on the basis of a general theory concerned with the decay and branching of arbitrary discontinuities. Stability boundaries are identified for decay processes in stable shock waves, isentropic rarefaction, compression waves, and tangential discontinuities. The evolution of a discontinuity with none of the normal stability boundaries is also considered. It is shown that such a wave would be stable with respect to small perturbations. It is also shown that shock waves that are not unstable do not exist, when the instantaneous decay of shock waves can be represented by other stable waves moving at different velocities but not overtaking each other. The possibility of observing the stable waves in laboratory experiments is discussed. A numerical analysis of the physical conditions for the development of a three-wave configuration along the front of an initial nondisintegrating shock wave showed that the criteria of stationarity and attenuation in the nondisintegrating shock are identical to the familiar criteria for stationarity and attenuation in weak deformations on the surface of a shock front. The weak deformations at the front surface were found using a series of linearized gasdynamic equations for the perturbations.
- Publication:
-
Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki
- Pub Date:
- February 1985
- Bibcode:
- 1985ZhETF..88..470K
- Keywords:
-
- Dynamic Stability;
- Perturbation Theory;
- Shock Wave Attenuation;
- Compression Waves;
- Isentropic Processes;
- Shock Fronts;
- Fluid Mechanics and Heat Transfer