Bifurcation analysis of the plane sheet pinch
Bifurcation analysis of the plane sheet pinch
复制标题
平面板材夹点分岔分析
DOI：
10.1103/physreve.61.2695
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发表时间：
1999
期刊：
影响因子：
--
通讯作者：
N. Seehafer
中科院分区：
文献类型：
--
作者：
J. Schumacher;N. Seehafer
对电驱动平板箍缩过程进行了数值分岔分析。导电率在整个片材上变化，从而允许静态基本状态在某个临界哈特曼数下不稳定。最不稳定的扰动是二维撕裂模。将整个问题限制在两个空间维度上，该模式被追踪到时间渐进稳定状态，事实证明，即使接近主要不稳定性发生的点，该状态对三维扰动也很敏感。通过改变薄板夹持参数，对二维定常撕裂模式状态进行了全面的三维稳定性分析。三维扰动的不稳定性被一个足够强的磁场在平衡的不变方向抑制。对于一个特殊的系统参数的选择，不稳定扰动状态的后续在其非线性演化，并发现接近三维稳态。
A numerical bifurcation analysis of the electrically driven plane sheet pinch is presented. The electrical conductivity varies across the sheet such as to allow instability of the quiescent basic state at some critical Hartmann number. The most unstable perturbation is the two-dimensional tearing mode. Restricting the whole problem to two spatial dimensions, this mode is followed up to a time-asymptotic steady state, which proves to be sensitive to three- dimensional perturbations even close to the point where the primary instability sets in. A comprehensive three- dimensional stability analysis of the two-dimensional steady tearing-mode state is performed by varying parameters of the sheet pinch. The instability with respect to three-dimensional perturbations is suppressed by a sufficiently strong magnetic field in the invariant direction of the equilibrium. For a special choice of the system parameters, the unstably perturbed state is followed up in its nonlinear evolution and is found to approach a three-dimensional steady state.