柱几何中采用极简方法的不稳定性：形式体系与旋转不稳定性
Instabilities in Cylindrical Geometry Using the Minimalist Approach: Formalism and Rotational Instabilities
- Department of Physics, National and Kapodistrian University of Athens（雅典国立卡波季斯特里安大学物理系）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究将线性稳定性分析的极简方法应用于柱几何流体与磁化理想等离子体，推导主方程并分析旋转流的轴对称不稳定性，阐明可压缩性对相关不稳定性稳定性特性的修正作用。
AI中文摘要：
将线性稳定性分析的极简方法应用于柱几何中的流体及磁化理想等离子体。该方法通过对单个一阶微分方程（即主方程）积分并结合合适边界条件得到色散关系。首先推导了一般未扰动态的主方程，该态具有径向变化的密度与压强、速度和磁场的轴向与方位分量，以及径向引力场。随后利用该形式体系分析带轴向磁场的旋转流，研究壁约束和界面驱动的轴对称不稳定性。除特定未扰动态的精确结果外，还在不可压缩和可压缩极限下用WKBJ方法得到近似色散关系。该分析涵盖离心、磁旋转和浮力驱动不稳定性作为特例，阐明可压缩性如何修正其稳定性特性。
英文摘要：
The minimalist approach for linear stability analysis is applied to fluids and magnetized ideal plasmas in cylindrical geometry. In this approach, the dispersion relation is obtained by integrating a single first-order differential equation - referred to as the principal equation - subject to appropriate boundary conditions. We first derive the principal equation for a general unperturbed state with radially varying density and pressure, axial and azimuthal components of both the velocity and magnetic field, and a radially directed gravitational field. We then use this formulation to analyze rotating flows with axial magnetic fields, addressing both wall-bounded and interface-driven axisymmetric instabilities. In addition to exact results for selected unperturbed states, we obtain approximate dispersion relations using the WKBJ method in the incompressible and compressible limits. The analysis encompasses centrifugal, magnetorotational, and buoyancy-driven instabilities as special cases, and it clarifies how compressibility modifies their stability properties.
