Modelling the Mixing and Erosion at the Head of Gravity Currents

由密度差驱动的流体运动是非常常见的。当冰箱打开时，或者在冬天打开窗户（通风）时，你可能已经注意到密集的冷空气从你的脚上掠过。即使你在房间的另一边，也能感受到这种效应。冷空气与上方较暖的空气混合时会稍微升温，但当它像洪水一样流过地板时，仍然保持足够的凉爽和独特。这些都是存在于我们的家庭，工业和更广泛的环境中的流体流动的一部分，称为重力流。通风流动对于了解病原体和疾病的传播很重要，冷锋基本上是相同的，但规模为100- 1000公里。在工业中，必须对危险气体的意外泄漏进行规划，并采取适当的防御措施。一个非常危险的重力流子集是粒子驱动流，悬浮粒子负载提供驱动密度并促进巨大的破坏力。例如，粉雪雪崩在山区是一种危险，很容易掩埋人和建筑物。火山碎屑密度流，由火山释放的灼热的火山灰云，流经地面，著名的埋葬庞贝，留下一个城市的人埋葬在火山岩。巨大的海底浊流，长度超过1000公里，移动速度高达10米/秒，将营养物质和碳带入深海，并摧毁了许多承载互联网数据或能源的电缆和管道。随着我们开发深海风力发电，较小的（尽管仍然很大）浊流将对英国构成越来越大的危险，而深海风力发电必须通过电缆连接回海岸。这些和其他发展的可行性取决于我们预测和减轻自然灾害的能力。水流的前沿将周围的流体推开，正是这里的动力学决定了水流前进的速度。此外，这一区域是混合的主要来源，对于某些海流来说，这一区域也是河床强烈侵蚀的区域。当电流与周围的流体混合时，它变得更加稀释，电流变得更大，同时具有降低的驱动密度。相反，当它侵蚀床时，驱动密度增加。因此，锋面对海流的前进有很强的控制作用，混合和侵蚀过程是其中的关键部分。然而，迄今为止，这些过程尚未被包括在设计用于预测这些电流的数学模型中，这限制了它们对短距离流动的适用性，使得混合基本上不会影响整体密度。此外，潮流的前沿是最危险的部分：使河床快速侵蚀的相同过程可以促进巨大的破坏力。在这个基础科学研究中，我将开发新的数学模型，捕捉重力流前沿的动态，包括混合和侵蚀过程。首先，使用新开发的技术进行的实验工作将为冷却、温度驱动的电流产生前所未有的高质量数据，测量涡流的细节，并在电流头部和整个过程中进行混合。更多的实验将侧重于捕捉沉积物驱动的电流侵蚀过程的细节。通过这些测量，我将在一个新的数学模型中捕捉头部动力学的重要方面，第一次包括混合和侵蚀过程。最后，头部的模型将与我之前开发的电流其余部分的模型相结合，以给出一个可以预测电流运动的完整模型。这个迫切需要的项目代表了我们对这类重要而危险的流动的理解和预测能力的重大飞跃。

Fluid movement driven by a density difference is very common. When a freezer is opened, or a window on a winter's day (a ventilation flow), you may have noticed that the dense, cold air rushes across your feet. This effect can be felt even if you are on the other side of the room, the cold air warming a little as it mixes with the warmer air above, but remaining sufficiently cool and distinct as it flows like a flood across the floor.These are part of a very broad family of fluid flows present across our homes, industries, and the wider environment, known as gravity-currents. Ventilation flows are important to understand for the spread of pathogens and disease, and cold-fronts are essentially the same but on the scale of 100-1000km. In industry, accidental spills of hazardous gas must be planned for, and suitable defences put in place. A very dangerous subset of gravity-currents are particle-driven currents, the suspended particle load providing the driving density and facilitating immense destructive power. For example, powder-snow avalanches are a hazard in mountainous regions, easily burying people and buildings. Pyroclastic density currents, searing hot clouds of ash released by volcanos and flowing out across the ground, famously buried Pompeii, leaving a city of people entombed in volcanic rock. Massive submarine turbidity-currents, >1000km long and moving at up to 10m/s, carry nutrients and carbon into the deep ocean, and have destroyed numerous cables and pipes carrying internet data or energy. Smaller (though still substantial) turbidity-currents will pose an increasing hazard to the UK as we develop deep-marine wind power, which must be connected back to shore by cables. The feasibility of these and other developments rely on our ability to predict and mitigate natural hazards. The front the current pushes aside the ambient fluid, and it is the dynamics here which determine the rate of advance of the current. In addition, this region is a principal source of mixing, and for some currents it is also a region in which there is intense erosion of the bed. As the current mixes with the fluid around it, it becomes more dilute, and the current becomes bigger while simultaneously having a reduced driving density. Conversely, as it erodes the bed the driving density increases. Thus, the front exerts a very strong control on the advance of the current, and the mixing and erosional processes are a critical part of this. However, to date these processes have not been included in the mathematical models that are designed to predict these currents, which has limited their applicability to flows over short distances so that the mixing does not substantially affect on the overall density. Additionally, the front of the current is the most dangerous part: the same processes that enable the rapid erosion of the bed can facilitate immense destructive power.In this fundamental scientific study, I will develop novel mathematical models that capture the dynamics of the front of a gravity-current, including the mixing and erosional processes. First, experimental work using newly developed techniques will yield data of unprecedented quality for a cool, temperature driven current, measuring the details of the vortices and mixing in both the head of the current and throughout. Additional experiments will focus on capturing the details of the erosional processes in sediment-driven currents. Informed by these measurements, I will capture the vital aspects of the dynamics of the head within a new mathematical model, for the first time including the mixing and erosional processes. Finally, the model of the head will be combined with a model for the rest of the current, which I developed previously, to give a complete model that can predict the motion of the current. This urgently required project represents a substantial leap-forward in our understanding and predictive power for this important and dangerous class of flows.