Mathematical modelling of lava flows undergoing rheological evolution

熔岩流是火山喷发最常见的产物，对财产和基础设施构成重大危险；因此，预测熔岩流路径是火山灾害管理的一个主要目标。此外，火山熔岩流可以作为一个“实验室”，探索如何将冷却和相变纳入对范围广泛的工业流体流动的模拟，这些流体流动也展示了流变学的演变(材料在外加应力下变形的方式)。最近在夏威夷(2020-2021年)、冰岛(2021年)和加那利群岛(2021年)发生的备受瞩目的喷发重新唤起了公众对这些流动的兴趣，并以研究现场数据和业余录像的形式为流体动力学模型的动机和验证提供了大量数据。熔岩侵位的预测需要流体动力学模型来解释流动过程中的流变性变化，特别是冷却地壳的逐渐形成。该项目将通过对火山熔岩流所表现出的三种复杂流动行为的模拟，实现我们模拟熔岩流侵位的能力的转变：泡状熔岩流的间歇性侵位，其中连续的脚趾膨胀、停滞和破裂以产生新的脚趾；在熔岩流边界形成固化堤坝，从而导致自我沟道化，增加向流动前沿的熔岩供应；以及在粘稠、一致的结壳和碎石、碎裂的结壳形成之间的过渡。拟议的项目将使用新的渐近、数值和实验方法的混合来模拟这些神秘的现象，利用我自己在粘塑性和浅层流动方面的专业知识，以及来自英国和国外的非牛顿流体动力学和火山学专家网络的支持。这项工作的成果将是改进正在经历流变演变的流动的建模，这将允许改进熔岩流动路径的预测，并在涉及冷却粘塑性流动的行业中更有效地生产过程，包括食品加工和3D打印。

Lava flows are the most common product of volcanic eruptions and pose a substantial hazard to property and infrastructure; as such, predicting the path of lava flows is a major goal in volcanological hazard management. Furthermore, volcanic lava flows can act as a "laboratory" for exploring how to include cooling and phase changes in the modelling of wide-ranging industrial fluid flows that also exhibit evolution of rheology (the manner in which a material deforms under imposed stress). Recent high-profile eruptions in Hawaii (2020-2021), Iceland (2021), and the Canary Islands (2021) have reinvigorated public interest in these flows, and have also provided significant quantities of data for the motivation and validation of fluid dynamical models, both in the form of research field data and in amateur videography. Prediction of lava emplacement requires fluid dynamic models that account for rheological changes during flow, particularly the progressive formation of a cooled crust. This project will achieve a transformation in our capacity to model lava flow emplacement through the modelling of three complex flow behaviours exhibited by volcanic lava flows: the intermittent emplacement of a Pahoehoe style lava flow in which successive toes inflate, stagnate and rupture to produce new toes; the formation of solidified levees at the boundaries of lava flows, resulting in self-channelisation and an enhanced supply of molten lava to the flow front; and transitions between ropy, consistent crust and rubbly, fragmented crust formation. The proposed project will use a mixture of novel asymptotic, numerical and experimental methods to model these enigmatic phenomena, using my own expertise in viscoplastic and shallow-layer flows and the support of a network of experts in non-Newtonian fluid dynamics and volcanology from the UK and abroad. The outcome of this work will be improved modelling of flows undergoing rheological evolution which will allow for improved prediction of lava flow paths and more efficient production processes in industries that involve cooling viscoplastic flows, including food processing and 3D printing.