COLLABORATIVE RESEARCH: Fingering convection at low Prandtl number

合作研究：低普朗特数下的指对对流

• 批准号: 0933057
• 负责人: Timour Radko
• 金额: $ 10万
• 依托单位: Naval Postgraduate School
• 依托单位国家: 美国
• 项目类别: Interagency Agreement
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-01-01 至 2013-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0933057&HistoricalAwards=false
• 关键词: COLLABORATIVE; RESEARCH; Fingering; convection; low

CBET - 0933759 /0933057 Garaud / Radko Fingering convection at low Prandtl number. Double-diffusive processes play an important role in mixing the upper ocean, and have been extensively studied in this context. Decades of experimental and theoretical research in the high-Prandtl (Pr) number regime characteristic of the heat/salt system have provided reliable parametrizations for the turbulent heat and salt fluxes induced by double-diffusive instabilities, as well as insight into the mechanisms leading to the formation of thermohaline staircases. Double-diffusive mixing is also thought to play a major role in the astrophysical context, and in particular in the interior of stars and giant planets. However, the applicability of parametrizations and analytical theories derived in the high-Pr regime to other regions of parameter space remains an entirely open question. Indeed, studies of the characteristics of linear and weakly nonlinear double-diffusive instability suggest that the low- Pr regime appropriate to the astrophysical context bears little resemblance to the aforementioned heat-salt system. The mechanism causing the saturation of the fingering instability is still undetermined; whether fingering convection leads to the formation of thermochemical staircases or not is an entirely open question. In short, double-diffusive transport remains one of the most uncertain components of global stellar/planetary evolution models. In this study, The PIs plan to carry out an extensive numerical and analytical study of fingering convection in the context of stellar/planetary interiors (Pr'á 1), address the points raised above and derive practical parametric formulae for the heat and compositional fluxes for use by the astrophysical community in global evolution models. The numerical tool the PIs intend to use has already been developed in the scope of a related but different NSF-funded study. Using this tool, the PI's team obtained the first ever evidence for 3D spontaneous thermohaline staircase formation. Since no low-Pr, 3D Direct Numerical Simulations of fingering convection have ever been performed, the PI's experimental results will be an invaluable point of comparison for all existing and future theories. The analytical tools the PIs intend to develop will be inspired by, and thus strive to extend, existing high-Pr work. Both astrophysical and oceanographic communities, supported by state-of- the-art numerical tools, will greatly benefit from this interaction. This study will contribute to UC-wide efforts in the development of the Fluid Dynamics and High-Performance Computing curricula by providing the opportunities for undergraduate training in research (Senior Thesis projects, and UC LEADS research opportunities) and by contributing to the construction of a fluid dynamics student experimental laboratory with inquiry-based learning educational techniques (as part of the Institute for Science and Engineer Educators program).

CBET - 0933759 /0933057 Garaud / Radko 低普朗特数下的双扩散过程在混合上层海洋中发挥着重要作用，并且在高普朗特数下已经进行了数十年的实验和理论研究。 Pr) 热/盐系统的数态特征为湍流热和盐通量提供了可靠的参数化由双扩散不稳定性引起的，以及对导致温盐阶梯形成的机制的深入了解，双扩散混合也被认为在天体物理背景中发挥着重要作用，特别是在恒星和巨行星的内部。然而，在高 Pr 范围中导出的参数化和分析理论对参数空间其他区域的适用性仍然是一个完全悬而未决的问题。事实上，线性和弱非线性特性的研究。双扩散不稳定性表明，适合天体物理背景的低 Pr 状态与上述热盐系统几乎没有相似之处，导致指状不稳定性饱和的机制仍不确定；指状对流是否会导致热化学阶梯的形成。简而言之，双扩散输运仍然是全球恒星/行星演化模型中最不确定的组成部分之一，PI 计划进行。在恒星/行星内部（Pr'á 1）的背景下对指对对流进行了广泛的数值和分析研究，解决了上述问题，并推导出热和成分通量的实用参数公式，供天体物理学界在全球演化中使用PI 打算使用的数值工具已经在 NSF 资助的一项相关但不同的研究范围内开发出来，PI 的团队使用该工具获得了 3D 自发温盐的第一个证据。由于尚未对指状对流进行过低 Pr 3D 直接数值模拟，因此 PI 的实验结果将成为所有现有和未来理论的宝贵比较点，PI 打算开发的分析工具将受到启发。并努力扩展现有的高 Pr 工作，在最先进的数值工具的支持下，这项研究将为整个加州大学在这方面的努力做出贡献。通过提供本科研究培训机会（高级论文项目和 UC LEADS 研究机会）以及通过探究式学习为流体动力学学生实验实验室的建设做出贡献，开发流体动力学和高性能计算课程教育技术（作为科学与工程教育者研究所计划的一部分）。