Dynamics of Lava Domes

Balmforth 0072521 熔岩穹丘是一种常见的地质构造，它们的几何形状使它们成为一种更简单的熔岩流。 此外，圆丘通常具有相对较低的长宽比，并且演化缓慢。 这些观测结果可以作为建立简单的膨胀和冷却流体圆顶的数学模型的成分;这个建议围绕着这样的模型的发展。 特别是，熔岩被认为是一种凝固，非牛顿流体与强烈的温度依赖materialqualities和内在的屈服应力。 问题的物理成分的广泛排列使得南极模型特别具有挑战性。 该项目利用圆顶简单的几何形状、缓慢的演化和低的长宽比来渐近地将控制方程简化为更简单的形式。这种简化了“浅熔岩方程”，就像“浅冰方程”被推导出来并广泛用于模拟冰盖和冰川一样。 差异的产生是因为熔岩的粘塑性性质，也因为凝固产生了覆盖在圆顶上的固体外壳，这可以显著地有助于力的平衡，特别是在圆盘的边缘。 数学方法与实验方法相辅相成，实验室流体被用作熔岩的模拟模型。 这两种方法都被用来探索圆顶的结构和演化，部分目的是了解更多关于熔岩作为流体的行为。 例如，一些圆顶失去轴对称，可能是一种内在的形态不稳定性，这种模式的形成过程中探索的光。 熔岩穹丘出现在地球和太阳系许多其他行星和卫星的许多地质环境中。 当富含晶体的岩浆通过火山口被推到大致水平的表面上时，这些结构就形成了，并且经常出现在火山爆发造成的陨石坑内。 与大多数其他熔岩流相比，阿拉瓦圆顶的形状特别简单。 因此，了解一般熔岩流的第一步是探索这些圆顶。 此外，尽管它们生长缓慢，但圆顶是自然灾害，因为它们可能是暴力和危险事件的发生地：圆顶可能破裂并释放出火山碎屑流出物（一种极热且快速移动的空气和灰烬流）中的压缩气体，或者在其外围坍塌，造成山体滑坡和泥石流。 该提案概述了一个数学和实验的方法来模拟熔岩圆顶。 目的是建立穹隆的结构和演化模型，并与实际地质构造进行比较。 通过以这种方式模拟圆顶，将更多地了解熔岩如何流动，最终这可能会提供与它们相关的危险的洞察力。

Balmforth0072521 Lava domes are a common geological formation, and theirgeometry sets them apart as one of the more simple types of lavaflow. Moreover, domes often have a relatively low aspect ratioand evolve slowly. These observations can be used as ingredientsin building simple mathematical models of expanding and coolingfluid domes; this proposal surrounds the development of suchmodels. In particular, lava is considered as a solidifying,non-Newtonian fluid with strongly temperature-dependent materialqualities and an intrinsic yield stress. The wide array ofphysical ingredients to the problem make the mathematicalmodelling especially challenging. The project exploits the simplegeometry, slow evolution and low aspect ratio of the dome toasymptotically reduce the governing equations to a simpler form.The reduction furnishes "shallow-lava equations," in much thesame way that the "shallow-ice equations" are derived andextensively used to model ice sheets and glaciers. Differencesarise because of the viscoplastic nature of silicic lava, andbecause solidification creates a solid crust overlying the domethat can contribute significantly to the balance of forces,especially at the disk's edge. The mathematical approach arecomplemented with an experimental one in which laboratory fluidsare used as analogue models of the lava. Both approaches are usedto explore the structure and evolution of the dome, partly withthe aim of learning more about how lava behaves as a fluid. Forexample, some domes lose axisymmetry in what might be anintrinsic morphological instability; this pattern formationprocess is explored in that light. Lava domes occur in many geological settings both on Earthand on many other planets and moons of the solar system. Thesestructures form when crystal-rich silicic magma is pushed upthrough vents onto roughly horizontal surfaces, and often occurinside the craters created by volcanic eruptions. The shape of alava dome is especially simple in comparison to most other lavaflows. Hence, a first step in understanding lava flows in generalis to explore those domes. Moreover, despite their slow growth,domes are natural hazards because they can be the setting ofviolent and dangerous events: domes can rupture and releaseconfined gas in a pyroclastic outflow (an extremely hot andfast-moving current of air and ash), or collapse at theirperipheries to create landslides and debris flows. The proposaloutlines a mathematical and experimental approach to themodelling of lava domes. The purpose is to build models of thedome's structure and evolution, and compare these models with thereal geological structures. By modelling the domes in this way,more will be learned about how lava flows, and ultimately thismay provide insight into the hazards associated with them.