Mixing regions, mixing barriers and a closure theory for baroclinic turbulence

众所周知，地球大气中的气流和海洋中的水流在很大范围内（从厘米到数千公里）都是湍流的。该提案旨在提高我们对存在于这些最大尺度上的湍流的理论和实践理解，即那些决定温带天气系统（气旋和反气旋）和海洋涡旋的出现、发展和混乱演变的湍流。了解大气天气系统（和海洋涡旋）与引导它们并从中获取能量的平均洋流之间的关系，是了解地球气候系统的核心。大气中的天气系统和海洋中的涡流从平均海流中提取能量的最重要过程之一就是斜压不稳定。如果电流不稳定到斜压不稳定，就会出现波状扰动，并且振幅增大。最终，这个波浪会“破裂”（类似于海滩上的水波），水流会变得湍流。本建议的重点是更好地理解由此产生的“斜压湍流”。由于影响地球大气和海洋的因素很多，而且观测资料相对较少，因此，关于斜压湍流的想法通常是通过将它们与理想化的流动数值模型的结果进行比较来检验的，在理想化的流动数值模型中，可以模拟相对“干净”的不稳定斜压流动的例子。我们的想法是理解斜压湍流的“纯粹”过程，就像它出现在模型流中一样，以便可以在与自然界中存在的所有外来过程隔离的情况下理解基本物理。这就是本文所采用的方法。PI先前提出了一种关于经历斜压湍流的流动行为的理论，并在一些初步试验中证明是成功的。目前的建议旨在通过将理论预测与上述数值模型模拟的结果进行比较，将理论扩展并验证一系列更现实的流动。采取渐进的方法来增加复杂性的动机是了解理论可能在哪里崩溃，如果发生这种情况，如何修改它。一个成功的结果将大大增加对波浪和平均流如何在大气和海洋中相互作用的理论理解，并且希望它将直接导致在海洋气候模型中表示海洋涡流效应的密切相关的想法（目前这些模型的尺度过于粗糙，无法捕捉涡流效应）。

The flow of air in Earth's atmosphere and water through the oceans is known to be turbulent on a wide range of scales (from centimetres to thousands of kilometres). The proposal aims to increase our theoretical and practical understanding of the turbulence that exists on the largest of these scales, i.e. those that determine the emergence, development and chaotic evolution of extratropical weather systems (cyclones and anti-cyclones), and oceanic eddies. Understanding the relationship between atmospheric weather systems (and oceanic eddies) and the mean currents that steer them, and from which they draw their energy, is central to understanding the Earth's climate system. One of the most important processes by which weather systems in the atmosphere and eddies in the ocean extract energy from the mean currents is known as baroclinic instability. If a current is unstable to baroclinic instability, a wave-like disturbance will emerge and grow in amplitude. Eventually this wave will `break' (in an analogous fashion to water waves on a beach) and the flow will become turbulent. The focus of the present proposal is to understand better the resulting `baroclinic turbulence'. Due to the many factors influencing the Earth's atmospheres and oceans, and the relative sparsity of observations, ideas relating to baroclinic turbulence are usually tested by comparing them with the results of idealised numerical models of flows in which relatively `clean' examples of unstable baroclinic flows can be simulated. The idea is to understand the `pure' process of baroclinic turbulence as it appears in the model flows, in order that the basic physics can be understood in isolation from all of the extraneous processes that are present in nature. This is the approach taken in the present work. A theory for the behaviour of flows experiencing baroclinic turbulence has been previously postulated by the PI and has proved successful in some preliminary tests. The current proposal aims to extend and verify the theory for a range of more realistic flows, by comparing theoretical predictions with the outcome of numerical model simulations as described above. The motivation in taking a gradual approach to additional complexity is to understand where the theory might break down, and if it does so, how it might then be modified. A successful outcome will greatly increase theoretical understanding of how waves and mean flows interact in the atmospheres and oceans, and it is hoped will lead directly to closely related ideas for representing the effects of ocean eddies in ocean climate models (which are currently too coarse in scale to capture eddy effects).