Random Waves and Vortices: Flow Decomposition and Energy Fluxes

这个项目是一项理论流体力学研究，旨在提高我们对小尺度湍流大气海洋过程的理解，这些过程在今天的全球尺度计算机模型中是无法解决的。该项目的关键组成部分是更好地了解流体中从大尺度到小尺度的湍流能量转移，以及湍流平流对海洋中被动漂浮装置的影响，目的是从昂贵的海洋测量中提取最大信息。总体而言，拟议的工作在流体力学、物理海洋学和动力气象学方面具有广泛的影响，其培训方面包括研究生和本科生。这些复杂系统的流体动力学特征是一个混合了湍流波和涡的非线性拼图，特别是在小尺度上，例如与亚中尺度海洋学有关的那些。在这里，经典的波-均值相互作用理论失效，不可能用全球计算模型直接数值模拟流体运动，需要诊断和预测模型的理论创新。在这方面，该项目力求通过多管齐下的办法开辟新的天地，在三个问题领域结合理论和数值模拟。首先，对旋转分层湍流中的三阶结构函数进行了基础性研究，目的是从稀疏的观测数据中更好地诊断光谱尺度能量通量。其次，最近的诊断波涡分解方法将被扩展到在一组随机拉格朗日示踪剂之后进行数据采集的日益重要的情况。第三，通过将某一慢变波的渐近守恒定律推广到更一般的波场，改进了波与涡相互作用的预测模型。这项拟议的研究要求进行非平凡的数学调查，涉及各种多维偏微分方程组、渐近分析、随机建模和数值计算，所有这些都着眼于与大气和海洋动力学有关的最终应用。这是应用数学和几个物理科学的不同分支之间的一次不平凡的技术转让。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

This project is a theoretical fluid dynamics study aimed at improving our understanding of turbulent atmosphere ocean processes at small scales, which are unresolvable in today's global-scale computer models. Key components of the project are the improved understanding of turbulent energy transfers from large to small scales in the fluid, and the effect of turbulent advection on passive floating devices in the ocean, which is aimed at extracting maximal information from costly oceanographic measurements. Overall, the proposed work has broad impacts within fluid mechanics, physical oceanography, and dynamical meteorology, and its training aspects include both graduate and undergraduate students. The fluid dynamics of these complex systems is characterized by a nonlinear jigsaw puzzle of intermingling turbulent waves and vortices, especially at small scales, such as those relevant to submesoscale oceanography, for instance. Here classical wave-mean interaction theory fails, direct numerical simulation of the fluid motion with global computational models is not possible, and theoretical innovations for diagnostic and predictive models are needed. In this connection the project seeks to break new ground with a multi-pronged approach that combines theory and numerical modelling in three problem areas. First, a fundamental study of third-order structure functions in rotating stratified turbulence is proposed, with the aim of better diagnosing spectral, scale-to-scale energy fluxes from sparse observational data. Second, a recent diagnostic wave- vortex decomposition method is to be extended to the increasingly important case of data acquisition following a set of random Lagrangian tracers. Third, a predictive model for interactions between waves and vortices is to be improved by generalizing a certain asymptotic conservation law for slowly varying waves to more general wave fields. The proposed research calls for non-trivial mathematical investigations that involves various systems of multi-dimensional PDEs, asymptotic analysis, stochastic modelling, and numerical computation, all with an eye towards ultimate applications in the real world that are relevant to atmosphere and ocean dynamics. This is a non-trivial technology transfer between different branches of applied mathematics as well as of several physical sciences.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.