Random and deterministic wave-vortex interactions in fluid dynamics

流体动力学中的随机和确定性波涡相互作用

• 批准号: 1312159
• 负责人: Oliver Buhler
• 金额: $ 37.2万
• 依托单位: New York University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-09-01 至 2017-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1312159&HistoricalAwards=false
• 关键词: Random; deterministic; wave; vortex; interactions

This is a theoretical and numerical study of nonlinear interactions between waves and vortices in two subject areas: atmosphere ocean fluid dynamics relevant to climate science, and plasma physics relevant to tokamak dynamics and nuclear fusion. Common to these interaction problems are the huge inherent scale separations between the different dynamical components of the flow, which render a direct numerical simulation hopeless and which also introduce a stochastic component to the system dynamics because the small-scale components are only partially observable. Hence the study involves the mathematical investigation of various systems of multidimensional nonlinear PDEs using a combination of asymptotic analysis, stochastic modeling, and numerical computation, all with an eye towards ultimate applications in the real world that are relevant to climate science and nuclear fusion. Specifically, the study consists of three projects. The first considers a special kind of small-scale internal gravity wave in the ocean and its interactions with mean currents near the sea floor, the second considers random particle motion induced by deep-ocean internal waves in the presence of forcing and dissipation, and the third investigates the wave-turbulence jigsaw puzzle posed by interactions between strong drift waves and strong zonal flows in the problem of plasma confinement in tokamaks.Atmosphere ocean dynamics relevant to climate science contains a vast span of active dynamical scales, from millimeters and milliseconds associated with sound waves to planetary scales and decades associated with large-scale ocean circulations, for example. All these scales are dynamically coupled together through a wide variety of nonlinear interactions and this is where fundamental mathematical theory can make a decisive contribution, namely by reducing these interactions into more tractable and understandable components that can then be simulated with significantly greater ease. Analogous comments apply to plasma dynamics that is relevant to fusion research and the behavior of tokamak devices. Hence, results from this theoretical study may feed into the future design of next generation atmosphere ocean forecasting systems for weather and climate, which is of great societal importance, and they should also strengthen the fundamental principles that feed into the design of nuclear fusion devices in tokamaks.

这是对波和涡旋之间非线性相互作用的理论和数值研究，涉及两个主题领域：与气候科学相关的大气海洋流体动力学，以及与托卡马克动力学和核聚变相关的等离子体物理学。这些相互作用问题的共同点是流动的不同动力分量之间存在巨大的固有尺度分离，这使得直接数值模拟毫无希望，并且还向系统动力学引入了随机分量，因为小尺度分量仅是部分可观察的。因此，该研究涉及结合渐近分析、随机建模和数值计算对各种多维非线性偏微分方程系统进行数学研究，所有这些都着眼于与气候科学和核聚变相关的现实世界中的最终应用。 具体来说，该研究由三个项目组成。第一个考虑了海洋中一种特殊的小尺度内部重力波及其与海底附近平均流的相互作用，第二个考虑了在存在强迫和耗散的情况下由深海内部波引起的随机粒子运动，以及第三研究了托卡马克等离子体约束问题中强漂移波和强纬向流之间相互作用所引起的波湍流拼图。与气候科学相关的大气海洋动力学包含广泛的活跃动力学尺度，例如，从与声波相关的毫米和毫秒到与大规模海洋环流相关的行星尺度和数十年。所有这些尺度通过各种非线性相互作用动态耦合在一起，这就是基础数学理论可以做出决定性贡献的地方，即通过将这些相互作用减少为更容易处理和理解的组件，然后可以更容易地进行模拟。类似的评论适用于与聚变研究和托卡马克装置的行为相关的等离子体动力学。因此，这项理论研究的结果可能会被用于下一代天气和气候大气海洋预报系统的未来设计，这具有重大的社会意义，并且它们还应该加强核聚变装置设计的基本原则。托卡马克。