Collaborative Research: CMG--Application of Multi-Scale and Stochastic Methods to Mesoscale Eddy Parameterization Schemes

非线性、多尺度系统（如湍流）被广泛认为是物理科学中最具挑战性的问题之一;海洋和大气的环流是具有巨大社会重要性的此类系统的例子。气候模式最重要的功能之一是准确地表示海洋中的盐作为盐、热、浮游植物、营养物和碳等标量场的时空分布。然而，海洋的环流是由波浪和湍流主导的，由于流体的非线性性质，波浪和湍流在许多尺度上相互作用。 这些系统具有大量的自由度，不能在计算模型中充分表示。因此，运动的“小”尺度的影响，（10公里和更少）通常参数化，使模型具有比真实的系统少得多的自由度。在这项研究中，数学家与地球物理流体动力学的背景，计划一个新的方法如何湍流表示在海洋环流模型。他们提出了两种方法：多尺度技术和拉格朗日随机模型。第一种方法概括了目前的做法，使用恒定的涡流扩散率，它将通过多尺度均匀化或随机偏微分方程的数学理论。第二种方法提供了一种手段，表示异常扩散时出现的相干结构，如涡流和射流占主导地位的流动。研究生和博士后将致力于这些跨学科的主题。

ABSTRACTOCE-0620874Nonlinear, multiscale systems such as turbulence are widely regarded as one of the most challenging problems in the physical sciences; the circulation of the ocean and atmosphere are examples of such systems which have tremendous societal importance. One of the most crucial functions of a climate model is to accurately represent the temporal and spatial distribution of scalar fields such as salt, heat, phytoplankton, nutrients and carbon within the ocean. However, the circulation of the ocean is dominated by waves and turbulence that operate on many scales which interact with each other due to the nonlinear nature of the fluid. These systems have a large number of degrees of freedom which can not be adequately represented in computational models. Thus, the effect of "small" scales of motion, (10's of kilometers and less) are typically parameterized so that models have many fewer degrees of freedom than the real system In this study, mathematicians with backgrounds in geophysical fluid dynamics, plan a fresh approach to how turbulence is represented in ocean general circulation models. They propose two approaches: multi-scale techniques and Lagrangian stochastic models. The first approach generalizes the current practice of using a constant eddy diffusivity and it will be developed through the mathematical theory of multiscale homogenization or random partial differential equations. The second approach provides a means of representing the anomalous diffusion that arises when coherent structures such as vortices and jets dominate the flow. A graduate student and postdoc will work on these interdisciplinary topics.