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: 0933759
• 负责人: Pascale Garaud
• 金额: $ 12.5万
• 依托单位: University of California-Santa Cruz
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 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=0933759&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 低普朗特数下的Garaud / Radko指状对流。双扩散过程在上层海洋混合中起着重要作用，并在这方面得到了广泛的研究。几十年的实验和理论研究的高普朗特（Pr）数制度的热/盐系统的特性提供了可靠的参数化的湍流热和盐通量引起的双扩散不稳定性，以及洞察到的机制，导致温盐楼梯的形成。双扩散混合也被认为在天体物理学中起着重要作用，特别是在恒星和巨行星的内部。然而，在高Pr政权的参数化和分析理论的适用性参数空间的其他区域仍然是一个完全开放的问题。事实上，对线性和弱非线性双扩散不稳定性特征的研究表明，适合天体物理背景的低Pr区与上述热盐系统几乎没有相似之处。导致指进不稳定性饱和的机制尚未确定;指进对流是否导致热化学阶梯的形成是一个完全悬而未决的问题。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。在这项研究中，PI计划在恒星/行星内部（Pr 'á 1）的背景下对指状对流进行广泛的数值和分析研究，解决上述问题，并推导出天体物理界在全球演化模型中使用的热量和成分通量的实用参数公式。PI打算使用的数字工具已经在NSF资助的相关但不同的研究范围内开发。利用这个工具，PI的团队获得了有史以来第一个3D自发热盐楼梯形成的证据。由于没有低Pr，三维直接数值模拟的指状对流曾经进行过，PI的实验结果将是一个宝贵的比较点，所有现有的和未来的理论。PI打算开发的分析工具将受到现有高PR工作的启发，从而努力扩展现有的高PR工作。天体物理学和海洋学界在最先进的数字工具的支持下，将大大受益于这种相互作用。这项研究将有助于加州大学范围内的努力，在流体动力学和高性能计算课程的发展，提供了机会，本科培训的研究（高级论文项目，和UC LEADS的研究机会），并有助于流体动力学学生实验实验室的建设与探究式学习教育技术（作为科学和工程师教育计划的一部分）。