CMG: Non-Hydrostatic Effects and New Diagnostics for the Long-Time Dynamics of Rotating and Stratified Flows

海洋和大气的动力受到地球自转和分层的强烈影响。在大气中，由于太阳的加热和地球引力的作用，较冷、较重的空气沉降到较热、较轻的空气下面。在海洋中，较冷、较咸的水位于较暖、较淡水的下面。旋转和分层的相对重要性取决于长度和时间尺度。例如，地球自转对飓风、急流和洋流等大规模结构的动力学至关重要，但对诸如积云和船舶产生的波浪等较小规模的运动影响不大。地球物理流的空间尺度范围很广，从数千公里到米，这是它们行为如此丰富、计算成本如此高昂、难以理解的原因之一。在某些尺度下，中等尺度的运动自组织产生较大尺度的结构，如飓风，而在另一些尺度下，能量从大尺度的风和潮汐转移到小尺度的湍流波动。在大尺度上，气流变成准二维的，运动主要平行于地球表面，而在小尺度上，它通常在三个方向上都是完全湍流的。目前用于研究海洋和大气的数学模型捕捉到了大尺度的流动，而忽略了小尺度的动态。即使在今天的计算机上使用最高的分辨率，这些模型也不能准确地预测长期的变化。例如，在千年海洋模拟中，由于对诸如深水混合和稠密水溢出（例如来自丹麦海峡）等小规模过程的代表性不足，重大误差会随着时间的推移而累积。这些错误表明，我们预测气候变化的能力存在重大障碍，因为在气候变化相对较快的时期，以前曾发生过大规模海洋环流的中断。因此，中尺度和小尺度运动在长时间大尺度动力学中起着重要的作用，这一点越来越清楚。本研究的目的是探讨旋转和分层流动中这种多尺度耦合的机制。数学模型和一个新的统计框架将被开发出来，并在洛斯阿拉莫斯国家实验室的一些世界上最大的可用计算机上进行计算机模拟测试。我们的理论与数值结合的方法为年轻科学家的培训提供了一个独特的机会，以发展下一代的海洋、大气和气候模式。

The dynamics of the oceans and the atmosphere are strongly influenced by the rotation of the earth and stratification. In the atmosphere, stratification results from solar heating coupled with earth's gravity, whereby colder, heavier air settles below warmer, lighter air. In the ocean, colder, saltier water lies below warmer, fresher water. The relative importance of both rotation and stratification depends on length and time scales. For example, the earth's rotation is critical to the dynamics of large-scale structures such as hurricanes, jet streams, and oceanic currents, but has a minor effect on smaller-scale motions such as cumulus clouds and waves generated by a ship.The wide range of spatial scales in geophysical flows, from thousands of kilometers to meters, is one reason why they are so rich in behavior, so costly to compute, and so difficult to understand. In certain scale regimes, intermediate-scale motions self-organize to generate larger-scale structures such as hurricanes, while in other regimes, energy is transferred from large-scale winds and tides to small-scale turbulent fluctuations. On large scales the flow becomes quasi-two-dimensional, with motions mainly parallel to the surface of the earth, whereas at small scales it is often fully turbulent in all three directions. Current mathematical models for studying the oceans and the atmosphere capture the large scales of the flow at the expense of removing small-scale dynamics. Even at the highest resolutions possible on today's computers, these models fail to accurately predict long-term variability. For example, in thousand-year ocean simulations, significant errors accumulate over time because of inadequate representation of small-scale processes such as deep-water mixing and dense-water overflows (e.g., from the Denmark Strait). Such errors indicate a significant obstacle for our ability to predict climate change, since breakdowns in the large-scale ocean circulation have previously occurred during relatively rapid changes in climate. Thus it is becoming increasingly clear that the intermediate-scale and small-scale motions play a significant role in long-time, large-scale dynamics.The goal of the proposed research is to probe the mechanisms for such multi-scale coupling in rotating and stratified flows. Mathematical models and a new statistical framework will be developed and tested with computer simulations on some of the largest available computers in the world at Los Alamos National Laboratory. Our combined theoretical and numerical approach provides a unique opportunity for the training of young scientists toward development of the next generation of ocean, atmosphere, and climate models.