Shape dynamics of melting ice: Experiments, simulations, modeling and analysis

地球上的冰储备正在以越来越快的速度融化。要解释这些变化对我们地球的健康意味着什么，就需要能够解释在巨大的长度和时间尺度范围内相互依存的复杂过程的模型。全球尺度气候模型的准确性取决于最基本尺度上的物理特性，例如冰的融化如何取决于其与液态水界面的形状以及当地的温度、盐度和流动条件。应用数学和计算数学以及数学建模提供了许多非常适合解决这些问题的方法。应用这些技术和开发专门用于冰融化的新技术可以提供改进气候模型所需的关键信息。更好地理解潜在的物理和数学也可以帮助解释自然冰的不同形状和模式，这可以从对冰的观察中推断出当地的环境条件。调查这些重要问题也为教育学生和培训研究人员提供了机会，从而有助于培养一支为解决这些问题和相关问题做好充分准备的劳动力。这些项目通过实验室实验、数值模拟、数学建模和分析来研究冰的融化动力学。研究计划的总体进展是从理想的环境，如在固定的远场温度下，在淡水中融化具有简单初始形态的固定物体，到涉及几何、温度和盐度变化的日益复杂的情况。进一步的扩展解决了额外的耦合，如融化引起的自由冰运动。实验将集中在精确测量的冰-水界面形式和运动的实验室设置中，初始几何形状，远场温度，和盐度剖面可以控制和系统地变化。直接数值计算将采用相场方法来模拟引起界面动力学的温度、流动和盐浓度场的演变。例如，建模将调用基于边界层理论的理想化，以导出与模式形成相关的移动边界描述和稳定性分析。所有方法都将相互结合，以针对目前对冰的演变形状如何反馈融化过程以及冰的形态如何用于推断环境条件的理解中的重大空白。该奖项反映了美国国家科学基金会的法定使命，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。

The Earth's ice reserves are melting with increasing rate. Interpreting what these changes mean for the health of our planet requires models that account for complex processes that act interdependently over immense ranges of length and time scales. The accuracy of global-scale climate models depends on the physics at the most fundamental scales, such as how the melting of ice depends on the shape of its interface with liquid water and the local temperature, salinity, and flow conditions. Applied and computational mathematics and mathematical modeling provide many methods that are well suited to addressing these problems. Applying such techniques and developing new ones specifically for ice melting can provide critical information needed to improve climate models. Better understanding the underlying physics and mathematics can also help to explain the diverse shapes and patterning of natural ice, which could allow local environmental conditions to be inferred from observations of ice. Investigating these important issues also provides opportunities to educate students and train researchers, thereby contributing to a workforce that is well prepared to tackle these and related problems.These projects investigate the melting dynamics of ice through laboratory experiments, numerical simulations, mathematical modeling, and analysis. The general progression of the research program is from idealized settings such as melting of fixed bodies with simple initial forms in fresh water at fixed far-field temperature to increasingly elaborate situations involving changes in geometry, temperature, and salinity. Further extensions address additional couplings such as melting-induced motions of free ice. Experiments will focus on accurate measurement of ice-water interface forms and motions in laboratory settings where the initial geometry, far-field temperature, and salinity profiles can be controlled and systematically varied. Direct numerical computations will employ phase-field methods to simulate the evolution of the temperature, flow, and salt concentration fields that give rise to the interfacial dynamics. Modeling will invoke idealizations based, for example, on boundary layer theory to derive moving-boundary descriptions and stability analyses that relate to pattern formation. All methods will be combined interactively towards targeting significant gaps in the current understanding of how the evolving shape of ice feeds back on the melting process and how the morphology of ice can be used to infer ambient conditions.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.