Mechanisms for the Formation of Coherent Structures from Small-Scale Turbulence in Anisotropic Flows

地球物理湍流可以用一系列包括波动和湍流的偏微分方程组来模拟。在每个模型中，涡旋的非波动运动对应于观察到的长期结构，例如对流层顶的急流、平流层的持续水平层和飓风。尽管在弱湍流展开中涡模和一阶波是解耦的，但数值模拟已经证明了从快波到各向异性涡模的产生。这些模拟建议对现有模型进行重大修改，以便只捕捉大尺度的动力。例如，它们显示了在强分层流动中垂直切变的水平流动模式的主导地位，目前大尺度模型中没有包括这些模式。我们的工作主要集中在(1)稳定性分析，以了解快速、小尺度湍流形成缓慢、大尺度相干运动的机制，以及(2)改进的常微分方程和偏微分方程组的发展，这些方程描述了缓慢变化的大尺度动力学，反映了数值模拟中观察到的物理现象。目前的大多数湍流模型基于各向同性理论，并假设小尺度湍流作为大尺度流动的能量汇聚。这类湍流模型用于数值预报，例如天气和气候变化。然而，自然界和工程流动中的湍流往往是各向异性的，例如，由于边界的存在。在这项研究中，我们重点研究了由强旋转和层结引起的各向异性，这两者都给出了波动运动。在各向异性波动-湍流系统中，湍流可以作为大尺度流动的能量来源。此外，小尺度随机波动往往自发地产生相干结构。自然界中的一个例子是大气中小尺度运动产生飓风。这项研究旨在从大气和海洋中的小尺度湍流中理解大尺度相干结构的产生。此外，将开发新的模型来捕捉这些现有模型所没有的物理现象。这一结果应该会影响我们预测海洋环流、天气和气候长期变化的能力。

Geophysical turbulence may be modeled by a hierarchy of partial differential equations including both waves and turbulence. In each model, the vortical, non-wave motionscorrespond to observed, long-lived structures such as the jet streamof the tropopause, the persistent horizontal layers of the stratosphere, and hurricanes. Despite decoupling of vortical modes and waves at first order in weak turbulence expansions, numerical simulations have demonstrated the generation of the anisotropic, vortical modes from fast waves. These simulations suggest major modifications tocurrent models designed to capture only the large-scale dynamics.For example, they show the dominance of verticallysheared, horizontal flow modes in strongly stratified flows, presently not included in large-scale models. Our workfocuses on (1) stability analyses to understand the mechanisms responsible for the formation of slow, large-scale coherent motions from fast, small-scale turbulence, and (2) thedevelopment of improved ordinary and partial differential equationsdescribing the slowly varying, large-scale dynamics, reflectingthe physics observed in the numerical simulations.Most current models of turbulence are based on isotropic theory, andassume that small-scale turbulence acts as a sink of energy forlarger-scale flows. Such turbulence models are used innumerical prediction, for example, of weather and climate change.However, turbulence in nature and in engineering flows is anisotropicmore often than not, for example, due to the presence ofboundaries. In this study, we focus on anisotropy induced bystrong rotation and stratification, both of which giverise to wave motions. In anisotropic wave-turbulence systems, turbulence may act as a source of energy for larger-scale flows.Furthermore, coherent structures oftenemerge spontaneously from small-scale, random fluctuations.One example in nature is the generation of hurricanesfrom smaller-scale motions in the atmosphere. This studyaims to understand large-scale, coherent-structure generationfrom small-scale turbulence in the atmosphere and oceans. Inaddition, new models will be developed to capture these physicalphenomena, absent in current models. The results should impact our ability to predict long-term variability in ocean-circulation,weather and climate.