COLLABORATIVE RESEARCH: Fingering convection at low Prandtl number

CBET-0933759/0933057低普朗特数下的Garaud/Radko指进对流。双扩散过程在上层海洋的混合中起着重要的作用，并在此背景下得到了广泛的研究。几十年来对热/盐系统高Prandtl(Pr)数区域特征的实验和理论研究，为双扩散不稳定性引起的湍流热、盐通量提供了可靠的参数化解，并深入了解了导致温盐阶梯形成的机制。双扩散混合也被认为在天体物理背景下发挥着重要作用，特别是在恒星和巨行星的内部。然而，在高Pr范围内派生的参数化和分析理论对参数空间的其他区域的适用性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，适合于天体物理背景的低Pr区域与前述的热-盐系统几乎没有相似之处。导致指进不稳定饱和的机制尚未确定；指进对流是否会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，PIS计划在恒星/行星内部(Pr‘á1)的背景下对指进对流进行广泛的数值和分析研究，解决上述提出的问题，并推导出实用的热通量和成分通量的参数公式，供天体物理界在全球演化模型中使用。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了。利用这一工具，PI的团队首次获得了3D自发温盐阶梯形成的证据。由于还没有对指进对流进行低Pr的3D直接数值模拟，PI的实验结果将是所有现有和未来理论的宝贵比较点。私人投资主任打算开发的分析工具将受到现有高公关工作的启发，并因此努力扩大现有工作。在最先进的数值工具的支持下，天体物理学和海洋学社区都将从这种互动中受益匪浅。这项研究将通过为本科生的研究培训(高级论文项目和加州大学主导的研究机会)提供机会，并通过建设一个采用探究式学习教育技术的流体动力学学生实验实验室(作为科学与工程教育人员研究所计划的一部分)，为加州大学在流体动力学和高性能计算课程的开发方面做出贡献。

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).