惯性波在地转剪切层中的反射-透射问题
The reflection-transmission problem for inertial waves on geostrophic shear layers
AI总结：
本文研究了惯性波与地转流的相互作用，发展了一个准二维分析模型，揭示了在薄地转剪切层中惯性波的反射和透射特性，展示了超临界剪切层作为低通滤波器的作用，允许低波数波通过。
摘要：
行星和恒星的流体区域中的惯性波在它们的动力学和演化的过程中通过能量、热量和角动量的传输以及化学物质的混合起重要作用。虽然在由刚体旋转规定的流动中惯性波的传播已被深入理解，但自然环境通常由对流或纬向流动特征化。在这些更现实的配置中，我们目前还不了解惯性波的传播及其传输特性。本文研究了惯性波与地转流的相互作用，迄今为止，这种相互作用仅通过射线理论或统计方法研究，其中波长假设远小于流体的长度尺度。我们开发了一个准二维分析模型，以研究存在局部地转剪切层时惯性波的反射和透射，并将理论发现与一组数值模拟进行比较。我们证明，与射线理论预测不同，即使在亚临界剪切层中也会发生部分反射，如果剪切层厚度远小于波长，在超临界剪切层中也可能发生近全透射的隧道效应。也就是说，超临界剪切层作为惯性波束的低通滤波器，允许低波数波通过。因此，我们的分析模型使我们能够预测惯性波与地转剪切层的相互作用，这些相互作用未被基于射线或统计的理论所涵盖，并且有助于理解完整波场在剪切层周围和内部的行为。
英文摘要：
Inertial waves in fluid regions of planets and stars play an important role in their dynamics and evolution, through energy, heat and angular momentum transport and mixing of chemicals. While inertial wave propagation in flows prescribed by solid-body rotation is well-understood, natural environments are often characterized by convection or zonal flows. In these more realistic configurations, we do not yet understand the propagation of inertial waves or their transport properties. In this work, we focus on the interaction between inertial waves and geostrophic currents, which has thus far only been investigated using ray theory, where the wave length is assumed to be small relative to the length scale of the current, or averaging/statistical approaches. We develop a quasi-two-dimensional analytical model to investigate the reflection and transmission of inertial waves in the presence of a localized geostrophic shear layer of arbitrary width and compare our theoretical findings to a set of numerical simulations. We demonstrate that, in contrast to ray theory predictions, partial reflections occur even in subcritical shear layers and tunnelling with almost total transmission is possible in supercritical shear layers, if the layer is thin compared to the wavelength. That is, supercritical shear layers act as low-pass filters for inertial wave beams allowing the low-wavenumber waves to travel through. Thus, our analytical model allows us to predict interactions between inertial waves and geostrophic shear layers not addressed by ray-based or statistical theories and conceptually understand the behaviour of the full wavefield around and inside such layers.
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