等熵大气中的非线性声学与激波动力学
Nonlinear acoustics and shock dynamics in isentropic atmospheres
AI总结：
本研究利用等熵分层大气中的精确简单波解，通过常微分方程描述波与激波演化，区分反射波与激波，并在中等马赫数下验证解析近似的准确性，同时揭示亚音速脉冲无法在不增熵的情况下解除质量束缚。
摘要：
非线性声学演化通常是在导致激波形成的波陡化背景下讨论的，并且在激波因其通道变窄或介质分层而持续增强的应用中特别受关注。精确的标度律适用于低振幅波和强激波，但连接这些阶段，或描述从一开始就非线性的波，通常需要数值模拟。我们利用平面平行、等熵且引力分层大气中的波由精确简单波解描述这一事实来解决该问题，这得益于在自由下落参考系中黎曼不变量的守恒。我们的解使我们能够区分反射波与形成激波的波，并利用常微分方程捕捉波和激波的演化。对于绝热指数$γ$的几个相关值，解是显式的；此外，对于$γ=3$，自由表面的非线性波反射可以解析描述。与流体动力学模拟的比较表明，我们的解析激波近似在中等（约几到15）马赫数范围内是准确的，且精度随绝热指数的增加而提高。我们的解还意味着，初始亚音速脉冲在不显著增加大气熵的情况下无法从大气中解除质量束缚。
英文摘要：
Nonlinear acoustic evolution is often discussed in the context of wave-steepening that leads to shock formation, and is of special interest in applications where the shock continues to strengthen due to a narrowing of its channel or the stratification of the medium. Accurate scalings govern low amplitude waves and strong shocks, but connecting these phases, or describing waves that are nonlinear from the outset, generally requires simulation. We address this problem using the fact that waves within a plane-parallel, isentropic and gravitationally stratified atmosphere are described by exact simple-wave solutions, thanks to the conservation of Riemann invariants in a freely falling reference frame. Our solutions enable us to discriminate waves that reflect from those that form shocks, and to capture wave and shock evolution using an ordinary differential equation. For several relevant values of the adiabatic index $γ$ the solutions are explicit; furthermore, nonlinear wave reflection from a free surface can be described analytically for $γ=3$. Comparison to hydrodynamic simulations shows that our analytic shock approximation is accurate up to moderate ($\sim$ few--15) Mach numbers, where the accuracy increases with the adiabatic index. Our solutions also imply that an initially subsonic pulse is unable to unbind mass from the atmosphere without significantly increasing its entropy.
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