摘要
我们在文[1]里对磁弧剪切作了数值解,得到了剪切速度ω和磁场B_z的分析解,但对二维速度(u,v)的振幅占δ′/ζ仅有只依赖于时间的近似解。本文在密度为常数条件下得到了磁弧剪切在线性演化阶段的较精确的解析解,比较了密度为常数和密度重力分层两种情形下的数值解,证实当β(=气压/磁压)很小(量级为10^(-2))时两者差别不大,因此本文结果近似可用于密度不为常数的实际太阳大气中的磁弧剪切动力学过程。解析解的主要结果是导出振幅δ′/ζ的高度依赖关系:随着时间增加,振幅δ′/ζ随高度下降越来越慢。这导致磁弧顶越升越高而脚根基本上不朝外移动,这样闭合的磁弧将有可能逐渐变为开场。
In paper (I) a numerical simulation was made for modelling the magnetic shearing dynamics, and the shearing velocity W and magnetic field Bz were given analytically. However, only an approximate solution has been found for the amplitude of the velocities (u, v). Now, an exact solution of magnetic shearing dynamics in the stage of linear development is obtained in this paper under the condition of constant gas-density. By comparing the numerical results in the cases of constant gas-density and gravity-stratified density, it is shown that the-difference between them is very small when the ratio β(=gas pressure/magnetic pressure) is of the order of 10-2. Therefore, our results can be applied to the shearing dynamic process in the actual solar atmosphere. With the help of the exact analytical solution, it is shown that the amplitude δ'/ξ, of velocities (u, v) grows almost linearly with time but declines slowly with height. As time goes on such decline is getting slower and slower. This peculiar behaviour makes the magnetic arch apex rise higher and higher while the feet of magnetic loops remain nearly fixed, thus the closed magnetic arch system may eventually become open.
