标题： 理想MHD波的精确非线性分解利用本征能量 显示英文标题

标题： Exact Nonlinear Decomposition of Ideal-MHD Waves Using Eigenenergies

摘要： 在本文中，我们引入了一种新的方法，用于将传播的非线性磁流体动力学（MHD）扰动精确分解为其与熟悉的慢波、阿尔芬波和快波本征模以及熵和磁场发散伪本征模相关的组件本征能量。 首先介绍了数学形式主义，说明如何利用理想MHD本征系统来构建总能量密度随时间变化的分解，以贡献来自本征模。 然后通过应用该方法到三个独立的非线性MHD模拟的输出来演示该分解方法。 对模拟的分析确认了该方法能够唯一地识别复合波场的组件波模。 显示慢波、阿尔芬波和快波的能量密度以与已知线性解和非线性特性（包括模式转换等过程）比较时所预期的方式演化。 在此过程中，识别并讨论了一些该分解方法数值实现中的潜在陷阱。 我们得出结论，所引入的精确非线性分解方法是理解MHD波分解本质以及分析和解释动态MHD模拟输出的强大而有前途的工具。 显示英文摘要

摘要： In this paper we introduce a new method for exact decomposition of propagating, nonlinear magnetohydrodynamic (MHD) disturbances into their component eigenenergies associated with the familiar slow, Alfv\'en, and fast wave eigenmodes, and the entropy and field-divergence pseudo-eigenmodes. First the mathematical formalism is introduced, where it is illustrated how the ideal-MHD eigensystem can be used to construct a decomposition of the time variation of the total energy density into contributions from the eigenmodes. The decomposition method is then demonstrated by applying it to the output of three separate nonlinear MHD simulations. The analysis of the simulations confirms that the component wave modes of a composite wavefield are uniquely identified by the method. The slow, Alfv\'en, and fast energy densities are shown to evolve in exactly the way expected from comparison with known linear solutions and nonlinear properties, including processes such as mode conversion. Along the way, some potential pitfalls for the numerical implementation of the decomposition method are identified and discussed. We conclude that the exact, nonlinear decomposition method introduced is a powerful and promising tool for understanding the nature of the decomposition of MHD waves as well as analysing and interpreting the output of dynamic MHD simulations.