标题： 讲义：天体物理流体动力学 显示英文标题

标题： Lecture notes: Astrophysical fluid dynamics

摘要： 这些讲义和例题是基于剑桥大学数学三部课程的内容。流体力学涉及非常广泛的天体物理现象，例如恒星和巨大行星的形成及其内部动力学、恒星和黑洞周围的喷流和吸积盘的工作机制，以及膨胀宇宙的动力学。在天体物理流体中可能重要的效应包括可压缩性、自引力以及磁场的动态影响，该磁场“冻结”在高导电性等离子体中。本课程中介绍并应用的基本模型是牛顿气体动力学和理想可压缩流体的磁流体动力学（MHD）。由于它们对于解析和数值求解方法以及物理解释的重要性， Governing equations 的数学结构和相关的守恒定律被详细探讨。线性和非线性波，包括激波和其他不连续性，都被讨论。超新星产生的球形爆炸波，涉及强激波，是一个可以通过解析方法解决的经典问题。具有球对称或轴对称的定常解揭示了恒星和盘状物风和喷流的物理机制。线性化方程决定了天体物理物体的振荡模式，以及它们的稳定性和对潮汐力的响应。 显示英文摘要

摘要： These lecture notes and example problems are based on a course given at the University of Cambridge in Part III of the Mathematical Tripos. Fluid dynamics is involved in a very wide range of astrophysical phenomena, such as the formation and internal dynamics of stars and giant planets, the workings of jets and accretion discs around stars and black holes, and the dynamics of the expanding Universe. Effects that can be important in astrophysical fluids include compressibility, self-gravitation and the dynamical influence of the magnetic field that is 'frozen in' to a highly conducting plasma. The basic models introduced and applied in this course are Newtonian gas dynamics and magnetohydrodynamics (MHD) for an ideal compressible fluid. The mathematical structure of the governing equations and the associated conservation laws are explored in some detail because of their importance for both analytical and numerical methods of solution, as well as for physical interpretation. Linear and nonlinear waves, including shocks and other discontinuities, are discussed. The spherical blast wave resulting from a supernova, and involving a strong shock, is a classic problem that can be solved analytically. Steady solutions with spherical or axial symmetry reveal the physics of winds and jets from stars and discs. The linearized equations determine the oscillation modes of astrophysical bodies, as well as determining their stability and their response to tidal forcing.