恒星内部隔音处理中的能量守恒和重力波：第一部分滞弹性近似
Energy Conservation and Gravity Waves in Sound-proof Treatments of Stellar Interiors: Part I Anelastic Approximations
摘要：
恒星内部的典型流动比声速慢得多。为了跟踪亚音速运动的缓慢演化，各种隔音方程被广泛使用，特别是在恒星天体物理流体动力学中。这些低马赫数方程包括滞弹性方程。一般来说，这些方程在近似绝热分层的区域（如恒星对流区）是有效的，但在亚绝热、稳定分层的恒星辐射内部可能无效。了解对流区和辐射内部之间的耦合是一个至关重要的问题，可能对太阳和恒星发电机理论有很强的影响，因为两者之间的界面，称为太阳的速跃层，在许多太阳发电机理论中起着至关重要的作用。本文研究了稳定层结大气中重力波的性质。特别是，我们探讨如何处理重力波在各种隔音方程。我们发现，一些滞弹性处理无法保存能量在稳定的分层大气，而不是保存伪能量，取决于分层，我们证明了这一点的数值。一个滞弹性方程组在所有的大气中都是能量守恒的，我们提供了将低马赫数滞弹性代码转换成这组方程的建议。
英文摘要：
Typical flows in stellar interiors are much slower than the speed of sound. To follow the slow evolution of subsonic motions, various sound-proof equations are in wide use, particularly in stellar astrophysical fluid dynamics. These low-Mach number equations include the anelastic equations. Generally, these equations are valid in nearly adiabatically stratified regions like stellar convection zones, but may not be valid in the sub-adiabatic, stably stratified stellar radiative interiors. Understanding the coupling between the convection zone and the radiative interior is a problem of crucial interest and may have strong implications for solar and stellar dynamo theories as the interface between the two, called the tachocline in the Sun, plays a crucial role in many solar dynamo theories. Here we study the properties of gravity waves in stably-stratified atmospheres. In particular, we explore how gravity waves are handled in various sound-proof equations. We find that some anelastic treatments fail to conserve energy in stably-stratified atmospheres, instead conserving pseudo-energies that depend on the stratification, and we demonstrate this numerically. One anelastic equation set does conserve energy in all atmospheres and we provide recommendations for converting low-Mach number anelastic codes to this set of equations.
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