摘要
本文用D′yakov的normal mocle方法讨论任意状态方程介质中的平面定常激波在二维小扰动下的稳定性,用直接的数学方法和新的物理考虑导出激波稳定性与参数i^2(dv/dp)_H在不同流场条件下的关系,结果表明此关系比较复杂,而过去的D yakov-Erpenbeck不稳定条件只是一个极端情形。尤其是发现在参数i^2(dv/dp)_H的两个稳定区域之间还存在不稳定区域,而这正对应于Griffiths等的实验中所观察到的不稳定激波,将结果用于完全气体激波时发现当绝热指数r>5/3时激波可能不稳定。通过计算比较,本文结果较成功地解释了Gritfiths等人的实验结论。
The stability of step shocks for arbitrary equation of state under two-dimensional perturbation is solved completely with new considerations of physics and mathematics based on the normal mode theory of D'yakov. It is found that the relation between stability and the shock parameter j2(dv/dP)H is not as simple as known before. The previous D'yakov-Er-penbeck instability condition is only an extreme case of this paper. A remarkable result is that there exists a range of instability between two ranges of stability on the axis of shock parameter j2 (dv/dP)H, and which is the just the range where the unstable shocks in the experiment by Griffiths and coworkers lie. Shocks in perfect gases could be unstable if the ratio of specific heats r>5/3.
出处
《力学学报》
EI
CSCD
北大核心
1989年第3期280-289,共10页
Chinese Journal of Theoretical and Applied Mechanics
关键词
激波
稳定性
冲击波
shock waves, 2-dimensional perturbation, temporal and spatial instability.
