激波稳定性(Ⅰ)  

SHOCK WAVE STABILITY (I)

作　　者：黄迎雷 崔季平[1] 

机构地区：[1]中国科学院力学研究所

出　　处：《力学学报》1989年第2期168-175,共8页Chinese Journal of Theoretical and Applied Mechanics

摘　　要：本文先用Ljapunov泛函方法求解在具有任意状态方程的流体介质中传播的一维平面定常激波在一维小扰动下的运动学稳定性问题。 得出激波的运动学稳定条件为—l≤i^2(dv/dp)_H≤1,其中—不i^2是激波Rayleigh线的斜率,(dv/dp)_H是Hugoniot线斜率。此条件与过去从唯象方法得到的条件一致,然后通过对这一条件能量意义的分析,提出一般的激波一维稳定性的能量原理,并由此得出激波能量稳定条件是—1≤i^2(dv/dp)_H≤l—p_o/p_l, 其中P_O、p_l分别是波前、波后压力,这个条件比运动学条件为优,由本文首次得到。The kinetic stability condition for step shocks under one-dimensional longi-tudinal perturbation in media with arbitrary equation of state has been solved by the Lja-punov functional method. This kinetic condition is found to be - 1≤j(dV/dP)E≤l, where - j2 is the slope of the Rayleigh line and (dV/dP)E the slope of the Hugoniot curve. This results agrees with Fowles' one. An energy principle of stability is proposed according to the physical meaning of the kinetic stability condition The derived energy condition of stability is -1≤j2(dV/dP)H≤1 - P0/P1, where P0, P1 are pressures aherd of the shock front and behind it respectively. This condition is more acceptable than the kinetic one.

关 键 词：激波 稳定性 运动学 流体介质 

分 类 号：O351.2[理学—流体力学]