Title: The reflection-transmission problem for inertial waves on geostrophic shear layers Show Chinese title

Title: 惯性波在地转剪切层上的反射-透射问题

Abstract: 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. Show Chinese abstract

Abstract: 流体区域中的惯性波在行星和恒星的动力学和演化中起着重要作用，通过能量、热量和角动量的传输以及化学物质的混合。 尽管由刚体旋转规定的流动中的惯性波传播已被很好地理解，但自然环境通常由对流或纬向流动所表征。 在这些更现实的配置中，我们目前还不了解惯性波的传播或其传输特性。 在本研究中，我们关注惯性波与地转流之间的相互作用，迄今为止，这仅通过射线理论进行过研究，在射线理论中假设波长相对于电流的尺度较小，或者通过平均/统计方法。 我们开发了一个准二维的解析模型，以研究局部地转剪切层存在下的惯性波的反射和透射，并将我们的理论结果与一组数值模拟进行比较。 我们证明，与射线理论的预测相反，即使在亚临界剪切层中也会发生部分反射，并且如果剪切层比波长薄，在超临界剪切层中可能发生几乎完全透射的隧穿。 也就是说，超临界剪切层对于惯性波束起到低通滤波器的作用，使低波数波能够通过。 因此，我们的解析模型使我们能够预测射线基或统计理论未涉及的惯性波与地转剪切层之间的相互作用，并概念性地理解此类层周围和内部整个波场的行为。