Sculpting of landforms by fluid flow

通过流体流动塑造地貌

• 批准号: 2704115
• 金额: --
• 依托单位: University College London
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2022
• 资助国家: 英国
• 起止时间: 2022 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2704115
• 关键词: Sculpting; landforms; fluid; flow

The interaction between fluid flow and surfaces which evolve in response to erosion, abrasion, chemical dissolution or freezing/melting effects is, in general, a challenging nonlinear free boundary problem: the flow field depends on the surface shape which, in turn, depends on the local fluid transport properties near the fluid-solid boundary. There is much interest in these processes, especially in a geological context where the interaction leads to striking features and patterns spanning lengthscales from centimetres to tens of kilometres. Some specific examples include ramified stream networks, ice-stars, ventifacts and the surface scalloping of caves, beneath ice floes and the Martian landscape. The flowing fluid in these examples can be either ocean, surface- or ground-water, or wind, and the shaping of the landscape can be through abrasion, erosion, sediment transport, precipitation or dissolution.In two-dimensions, and assuming irrotational flow of inviscid fluid and that the surface evolves slowly in comparison to the timescale associated with the fluid flow, the free boundary problems described above can be formulated in terms of a conformal map from some canonical domain with fixed boundaries to the physical domain with an evolving boundary representing the fluid-solid interface. The mathematical task then becomes one of determining the time-dependent map. It can be shown that the map satisfies a Polubarinova-Galin type equation with forcing dependent on the 'physics' of the erosion process e.g. abrasion, melting.This PhD project will formulate and solve a series of problems using a combination of analytic, asymptotic (e.g. early/late times) and numerical methods (e.g. reducing the Polubarinova-Galin to a high-order system of coupled ODEs). A variety of initial surfaces will be considered e.g. circular/elliptical objects, flat surfaces; and forcing types e.g. normal velocity of the interface being proportional to the fluid pressure.The effect of shed and trapped vortices is of special interest: their inclusion in the flow about arbitrary shaped bodies will be computed using Laplacian 'fast' solvers of the type recently pioneered by Trefethen and co-workers. Such methods are also capable of computing conformal maps to canonical domains, opening up the possibility of computing the evolution of evolving bodies in the presence of vortices. It will be interesting to determine if the presence of trapped vortices gives rise to sculpted surfaces with 'sharp' edges as are commonly observed in some desert landscapes and the Martian surface.The project will be of interest to researchers in applied complex analysis, fluid mechanics, vortex dynamics and applied mathematicians working on free boundary problems. The project is also likely to have interdisciplinary appeal to geographers, Earth and planetary scientists.The research falls under the EPSRC theme 'Fluid dynamics and Aerodynamics'.

通常，流体流与表面之间的相互作用是响应侵蚀，磨损，化学溶解或冻结/熔化效应而演变的，这通常是一个具有挑战性的非线性自由边界问题：流场取决于表面形状，取决于该表面形状，进一步取决于局部流体运输的流体传输特性。对这些过程非常感兴趣，尤其是在地质环境中，相互作用会导致从厘米到数十公里的长度尺度的引人注目的特征和图案。一些具体的例子包括流分流网络，冰棒，预防性和洞穴的表面扇贝，冰上浮标和火星景观。这些例子中流动的流体可以是海洋，表面或地下水或风，景观的形状可以是通过磨损，侵蚀，侵蚀，沉积物的传输，沉积物，降水或溶解。在二维中，并假设与毫无疑问的液体相比，与某些图表相比，表面逐渐逐渐与流动性流动相比，与流动性流动相关的情况相比，与流体流动相关的相关性，与界面相关，则可以逐渐形成，以上的范围是流动性流动的术语，而界限的范围则是差异，而在范围内则可以通过界限的范围进行了差异，而界限的范围则是在界限上的自由流动。具有固定边界的物理域的规范域，具有不断发展的边界，代表流体固定界面。然后，数学任务成为确定时间相关的映射之一。可以证明，该地图满足了polubarinova-galin型方程，并依靠侵蚀过程的“物理学”，例如磨损，融化。该博士项目将使用分析，渐近学（例如早期/晚期）和数值方法（例如将polubarinova-galin降低到偶联ODE的高阶系统）的组合来制定和解决一系列问题。各种初始表面将被视为，例如圆形/椭圆形物体，平面；并强迫类型，例如与流体压力成正比的界面的正常速度。棚和被困涡旋的效果具有特殊的兴趣：将使用laplacian的“快速”求解器计算出围绕任意形状物体的流动，这些旋转的速度将使用Trefethen和Trefethen和Fo-workers pioneye的类型进行计算。此类方法还能够计算出与规范域的共形图，从而开放了在存在涡流的情况下计算不断发展的物体演变的可能性。确定捕获涡流的存在是否会引起具有“锋利”边缘的雕刻表面，就像在某些沙漠景观和火星表面所观察到的那样。在应用复杂分析，流体机械，涡流动力学和应用数学家处理自由边界问题方面，研究人员将对研究人员感兴趣。该项目还可能对地理学家，地球和行星科学家具有跨学科的吸引力。该研究属于EPSRC主题“流体动力学和空气动力学”。