Random Waves and Vortices: Flow Decomposition and Energy Fluxes

该项目是一项理论流体动力学研究，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无法解决。 该项目的关键组成部分是更好地了解湍流能量在流体中从大尺度到小尺度的转移，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限度的信息。 总体而言，拟议的工作具有广泛的影响，在流体力学，物理海洋学和动力气象学，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混合湍流波和涡旋的非线性拼图，特别是在小尺度上，例如与中尺度海洋学有关的那些。 在这里，经典的波均相互作用理论失败，直接数值模拟的流体运动与全球计算模型是不可能的，诊断和预测模型的理论创新是必要的。 在这方面，该项目寻求以多管齐下的方法开辟新天地，在三个问题领域将理论和数值模拟相结合。首先，三阶结构函数在旋转分层湍流的基础研究提出，更好地诊断光谱，尺度到尺度的能量通量从稀疏的观测数据的目的。其次，最近的诊断波涡分解方法是扩展到数据采集后的一组随机拉格朗日示踪剂的日益重要的情况下。第三，预测模型之间的相互作用波和涡是通过推广一定的渐近守恒定律缓慢变化的波更一般的波场得到改善。 拟议的研究要求非平凡的数学调查，涉及各种系统的多维偏微分方程，渐近分析，随机建模和数值计算，所有着眼于最终的应用程序在真实的世界是相关的大气和海洋动力学。这是应用数学不同分支之间以及几个物理科学之间的重要技术转让。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值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.