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

地球物理湍流可以用包含波和湍流的偏微分方程的层次来模拟。在每一种模式中，涡旋的、非波动的运动都与观测到的、长期存在的结构相对应，如对流层顶的急流、平流层的持续水平层和飓风。尽管在弱湍流膨胀中，一阶涡型和波存在解耦，但数值模拟已经证明了由快波产生的各向异性涡型。这些模拟表明，对目前设计的只捕捉大规模动力学的模型进行了重大修改。例如，它们显示了在强分层流动中垂直剪切和水平流动模式的优势，目前尚未包括在大尺度模型中。我们的工作重点是(1)稳定性分析，以了解从快速，小规模湍流形成缓慢，大规模相干运动的机制；(2)改进的常微分方程和偏微分方程的发展，描述缓慢变化的大规模动力学，反映在数值模拟中观察到的物理现象。目前大多数湍流模型都是基于各向同性理论，并假设小尺度湍流作为大尺度流动的能量汇。这种湍流模式被用于数值预测，例如天气和气候变化。然而，在自然界和工程流动中，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，我们重点研究了强旋转和分层引起的各向异性，这两者都引起了波浪运动。在各向异性波湍流系统中，湍流可以作为大尺度流动的能量来源。此外，连贯结构往往自发地从小规模的随机波动中产生。自然界的一个例子是大气中较小尺度的运动产生飓风。本研究旨在了解大气和海洋中的小尺度湍流产生的大尺度、相干结构。此外，将开发新的模型来捕捉这些物理现象，目前的模型中没有。研究结果将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.