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

湍流等非线性多尺度系统被广泛认为是物理科学中最具挑战性的问题之一；海洋和大气的环流就是这种具有巨大社会重要性的系统的例子。气候模型最重要的功能之一是准确地表示标量场的时空分布，如海洋中的盐、热、浮游植物、营养物质和碳。然而，海洋的环流是由波浪和湍流控制的，它们在许多尺度上起作用，由于流体的非线性性质，它们相互作用。这些系统具有大量的自由度，无法在计算模型中充分表示。因此，“小”运动尺度（10公里或更小）的影响通常被参数化，因此模型的自由度比实际系统少得多。在本研究中，具有地球物理流体动力学背景的数学家计划采用一种新的方法来表示湍流如何在海洋环流模型中表示。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使用恒定涡流扩散率的做法，并将通过多尺度均匀化或随机偏微分方程的数学理论来发展。第二种方法提供了一种表示异常扩散的方法，这种扩散是在涡旋和射流等相干结构主导气流时出现的。研究生和博士后将研究这些跨学科课题。

ABSTRACTOCE-0620956Nonlinear, 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.