磁流体力学激波的特征速度

根据磁流体力学间断面的守恒条件与磁流体力学单波方程的相似性,引入了一个称为磁流体力学激波特征速度的物理量,它是激波在波前后两侧介质中传播速度的几何平均值,当激波很弱时,它趋近于磁流体力学波的速度。本文导出一组以此特征速度为强度参数的激波跃变公式,形式上与单波的公式组非常相像,从而简化了激波跃变量的计算。其中密度跃变公式本身解析地证明:磁流体力学激波与磁流体力学波传播速度之间的关系是由激波是压缩波这一特性直接决定的。 

CHARACTERISTIC VELOCITY OF MHD SHOCK

According to the similarity between the boundary conditions on the MHD discontinuity and the equations of the MHD simple wave, a physical quantity U_* called the characteristic velocity of MHD shock has been introduced. U_* is defined by Eq. (4) as the ratio of the jump of total presure p* to that of density p, and equal to the geometric mean value of the shock velocities Wrelative to the up and down streams (Eq. (5)), approaching to the MHD wave velocity Uin the weak shock limit.The system of equations (7) express the shock relations with U_* as the strengthparameter, where u, v =H/√4πρ and U± are respectively the velocity of fluid relativeto the shock front, and of the Alfven and the magnetosonic waves. These relations simplify the usual shock calculations and degenerate into the formulae for the MHD simple wave (Eq. (11)) in the infinitesimal jump limit.The fast, slow, and intermediate shock can be distinguished by Eq. (12-a, b, c) respectively. It is interesting to note that the jump formulae (7-a) and (13) show explicitly the transmission relations among the various modes of MHD shock and wave (Eq. (16-a, b, c) for the above three modes respectively), which are nothing but the immediate consequence of the compressive nature of shocks together with the conservation of mass (Eq. (14) and Eq. (15)). However, it needs a lengthy derivation to prove Eq. (16) without introducing U_*.