Instability of a convergent spherical shock wave
Abstract
The self-similar solution of the gasdynamic problem involving a convergent spherical shock wave is investigated for stability in the linear approximation. Arbitrary small perturbations of the flow are expanded in a generalized-spherical-harmonic series; and the eigenvalues of the differential equations characterizing the rate of growth of perturbations in the case of several lower spherical harmonics are determined numerically. It is shown that the shock wave is unstable with respect to small asymmetric perturbations. Finally, a method is described for the numerical determination of complex eigenvalues of boundary value problems described by a singular system of differential equations.
- Publication:
-
Zhurnal Vychislitelnoi Matematiki i Matematicheskoi Fiziki
- Pub Date:
- December 1982
- Bibcode:
- 1982ZVMMF..22.1468B
- Keywords:
-
- Computational Fluid Dynamics;
- Convergence;
- Flow Stability;
- Mach Cones;
- Shock Waves;
- Spherical Waves;
- Approximation;
- Differential Equations;
- Eigenvalues;
- Gas Dynamics;
- Linear Equations;
- Fluid Mechanics and Heat Transfer