Geophysical wave-vortex interactions and turbulence

这项流体动力学研究旨在提高对小尺度湍流大气海洋过程的理论理解，这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提高对流体中大尺度和小尺度之间湍流能量传递的理解。 这涉及到墨西哥湾流等水流系统与目前全球海洋计算机模型无法看到的快速波浪运动之间的强烈相互作用。总体而言，拟议的工作在流体力学，物理海洋学，其培训方面包括研究生和本科生广泛的影响。这些复杂系统的流体动力学的特点是混合湍流波和涡的非线性拼图，特别是在小尺度，如那些相关的亚中尺度海洋学，例如。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，本提案寻求以理论和数值模拟相结合的多管齐下的办法开辟新天地。首先，利用一种新的波动作用对流扩散理论研究了平衡平均流折射作用下湍流内波谱的长期演化。第二，利用从广义拉格朗日平均理论导出的新的波-平均相互作用方程，研究内波与平衡平均流之间强有力的双向相互作用。这些方程考虑了双向的强相互作用：波感受到平均流，反之亦然。 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 fluid dynamics study is aimed at improving the theoretical understanding of turbulent atmosphere ocean processes at small scales, which are unresolvable in today's global-scale computer models. The key components of the project are the improved understanding of turbulent energy transfers between large and small scales in the fluid. This involves vigorous interactions between current systems like the Gulf Stream and fast wave motions that cannot be seen by current global ocean computer models. Overall, the proposed work has broad impacts within fluid mechanics, physical oceanography, 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 present proposal seeks to break new ground with a multi-pronged approach that combines theory and numerical modelling. First, the long term evolution of turbulent internal wave spectra under refraction by the balanced mean flow is studied using a novel wave action advection-diffusion theory. Second, vigorous two-way interactions between internal waves and the balanced mean flow are studied using new wave-mean interaction equations derived from generalized Lagrangian-mean theory. These equations allow for strong interactions that cut both ways: the waves feel the mean flow and vice versa. This is an important but understudied regime for submesoscale oceanography.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.