Metastability of Geophysical Turbulent Flows

地球物理湍流的亚稳定性

• 批准号: 2280388
• 金额: --
• 依托单位: Aston University
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2019
• 资助国家: 英国
• 起止时间: 2019 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2280388
• 关键词: Metastability; Geophysical; Turbulent; Flows

The dynamics of geophysical turbulent flows, such as the Earth's atmosphere and oceans play a critical role in determining the long-term climate of our planet. Therefore, the understanding and modelling of their long-term mean dynamics becomes increasingly important for studying the effect of climate change. However, the equations of motions of these systems are incredibly complex and require high resolution numerical simulations computed over long computation times in order to acquire long-term flow statistics. I propose a PhD project that builds upon theory developed by my MSc supervisor Dr Jason Laurie concerning the prediction of mean flow profiles in these geophysical flows [1,2]. The plan of the project will be to develop a kinetic theory approach [3] to determine a stochastic Reynolds equation for the mean flow dynamics that depends on the Reynolds stresses of the underlying turbulent fluctuations. We will go beyond the typical quasi-linear approximation to include stochastic feedback correlated to the underlying turbulence. This will yield a set of equations that will be highly accurate, and computationally efficient and applicable to studying metastability using large deviation and instanton methods [4]. The benefits of this approach could be substantial for climate scientists. Indeed, the problem of modelling these phenomena typically necessitates the use of parallel computing, and as such we plan to develop new CUDA-enabled high-performance parallel codes using the computational facilities of Dr Jason Laurie. The project will further allow for me to build upon the point-vortex theory I have been working on with Dr Laurie during my MSc by Research at Aston University. Our point-vortex calculations can be used to study the dynamics of idealised setups of 2D classical and quantum turbulence and can be used to gain further insight into the mathematics regarding vortex scattering and sound emission. I have worked with Dr Laurie during my MSc by Research at Aston University on point-vortex dynamics. This project has given me an extensive introduction to fluid dynamics and theoretical physics as a whole; including topics such as Hamiltonian mechanics, phase-plane analysis, solutions of elliptic integrals, turbulence, vortex dynamics, etc. For this project, I have developed substantial experience in numerical methods and programming in C++ that will prove invaluable in this PhD position. The PhD project will provide a natural progression of my research interests in fluid mechanics and geophysical turbulence and further develop my scientific computing skills. I undertook the MSc by Research at Aston University following my undergraduate BSc in Mathematics, also at Aston University, in which I achieved the result of a high first class with honours. It was during this time that I developed my understanding of various different aspects of advanced mathematics, for example; chaos and dynamical systems, probabilistic modelling, numerical methods, and more.

地球物理湍流的动力学，例如地球的大气层和海洋，在决定地球的长期气候方面发挥着关键作用。因此，对其长期平均动态的理解和建模对于研究气候变化的影响变得越来越重要。然而，这些系统的运动方程非常复杂，需要在很长的计算时间内进行高分辨率数值模拟才能获得长期的流量统计数据。我提出了一个博士项目，该项目建立在我的硕士导师 Jason Laurie 博士开发的关于这些地球物理流中平均流量剖面预测的理论的基础上 [1,2]。该项目的计划将是开发一种动力学理论方法 [3] 来确定平均流动动力学的随机雷诺方程，该方程取决于潜在湍流波动的雷诺应力。我们将超越典型的准线性近似，包括与潜在湍流相关的随机反馈。这将产生一组高精度、计算效率高且适用于使用大偏差和瞬子方法研究亚稳态的方程[4]。对于气候科学家来说，这种方法的好处可能是巨大的。事实上，对这些现象进行建模的问题通常需要使用并行计算，因此我们计划使用 Jason Laurie 博士的计算设施开发新的支持 CUDA 的高性能并行代码。该项目将使我能够进一步建立点涡理论，这是我在阿斯顿大学攻读硕士学位期间与劳里博士一起研究的。我们的点涡计算可用于研究二维经典和量子湍流的理想化设置的动力学，并可用于进一步深入了解有关涡旋散射和声发射的数学。在阿斯顿大学攻读点涡动力学研究硕士学位期间，我曾与 Laurie 博士一起工作。这个项目让我对流体动力学和理论物理有了全面的了解；包括哈密顿力学、相平面分析、椭圆积分解、湍流、涡动力学等主题。在这个项目中，我在数值方法和 C++ 编程方面积累了丰富的经验，这些经验将在这个博士职位中证明是无价的。该博士项目将使我在流体力学和地球物理湍流方面的研究兴趣自然发展，并进一步发展我的科学计算技能。我在阿斯顿大学获得数学本科学士学位后，又在阿斯顿大学攻读了研究型硕士学位，并以优异的成绩获得了一等奖。正是在这段时间里，我发展了对高等数学各个不同方面的理解，例如：混沌和动力系统、概率建模、数值方法等等。