论文标题
在分层，可变区域和气氛中的线性和非线性声学上
On Linear and Nonlinear Acoustics in Stratified, Variable-Area Ducts and Atmospheres, and Lighthill's Proposition
论文作者
论文摘要
我们考虑在一维流的限制下，在可变区域的通道内的分层静水体流体中考虑线性和非线性波。我们得出了与波浪光度有关的Riemann不变性的修改版本。该数量在线性理论中遵守一个简单的动力学方程，从中可以很容易地辨别出波浪反射规则。并且在高频限制中是绝热的保守。根据Lighthill的建议，我们将线性绝热不变性应用于预测轻度的非线性波。这只会造成中等错误。我们发现，Lighthill的冲击形成标准基本上是主要的冲击，以及高频波内的冲击。我们得出的结论是，在复杂的环境（如恒星的信封）中，可以使用近似不变性来准确预测低振幅声脉冲的自我渗透以及弱冲击的耗散模式。我们还为有限类别的问题确定了完全非线性解决方案。
We consider linear and nonlinear waves in a stratified hydrostatic fluid within a channel of variable area, under the restriction of one-dimensional flow. We derive a modified version of Riemann's invariant that is related to the wave luminosity. This quantity obeys a simple dynamical equation in linear theory, from which the rules of wave reflection are easily discerned; and it is adiabatically conserved in the high-frequency limit. Following a suggestion by Lighthill, we apply the linear adiabatic invariant to predict mildly nonlinear waves. This incurs only moderate error. We find that Lighthill's criterion for shock formation is essentially exact for leading shocks, and for shocks within high-frequency waves. We conclude that approximate invariants can be used to accurately predict the self-distortion of low-amplitude acoustic pulses, as well as the dissipation patterns of weak shocks, in complicated environments such as stellar envelopes. We also identify fully nonlinear solutions for a restricted class of problems.
