二维等温C激波中的阻力不稳定性
The Drag Instability in a 2D Isothermal C-shock
摘要：
本文将顾和陈对一维垂直等温C激波中阻力不稳定性的线性分析推广到典型的恒星形成云环境中的二维垂直和斜向C激波。导出了不稳定模的简化色散关系。我们发现，阻力不稳定性的模式属性一般取决于横向（垂直于激波流）的纵向（沿激波流）的波数比。对于横向大尺度模式，二维激波中的阻力不稳定性的增长率和波频率与一维激波中的相似。对于横向小尺度模式，阻力不稳定性的特征在于主要沿横向方向与声学模式耦合的不稳定模式。当激波垂直或倾斜时，存在一个缓慢传播的模式，它可能会发展成一个非线性区域，并有助于不稳定性的最大增长。相反，当激波更倾斜时，这种缓慢传播的不稳定模式消失，并且阻力不稳定性的最大增长可能来自横向大尺度模式（即，几乎1D模式）。在我们考虑的所有情况下，密度扰动的幅度明显大于速度和磁场扰动的幅度，这意味着密度增强控制了不稳定性的线性区域中的动力学。线性分析中的几个问题，以及可能的天体物理意义，也作了简要的讨论。
英文摘要：
We extend the linear analysis of the drag instability in a 1D perpendicular isothermal C-shock by Gu & Chen to 2D perpendicular and oblique C-shocks in the typical environment of star-forming clouds. Simplified dispersion relations are derived for the unstable modes. We find that the mode property of the drag instability generally depends on the ratio of the transverse (normal to the shock flow) to longitudinal (along the shock flow) wavenumber. For the transversely large-scale mode, the growth rate and wave frequency of the drag instability in a 2D shock resemble those in a 1D shock. For the transversely small-scale mode, the drag instability is characterized by an unstable mode coupled with an acoustic mode primarily along the transverse direction. When the shock is perpendicular or less oblique, there exists a slowly propagating mode, which can potentially grow into a nonlinear regime and contribute to the maximum growth of the instability. In contrast, when the shock is more oblique, this slowly propagating unstable mode disappears, and the maximum growth of the drag instability is likely contributed from the transversely large-scale mode (i.e., almost 1D mode). In all cases that we consider, the magnitude of the density perturbations is significantly larger than that of the velocity and magnetic field perturbations, implying that the density enhancement governs the dynamics in the linear regime of the instability. A few issues in the linear analysis, as well as the possible astrophysical implications, are also briefly discussed.
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