A dynamical systems 'basis' for vortex interactions via differentiable programming and machine learning

通过可微分编程和机器学习实现涡旋相互作用的动力系统“基础”

• 批准号: 2435641
• 金额: --
• 依托单位: University of Edinburgh
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2020
• 资助国家: 英国
• 起止时间: 2020 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2435641
• 关键词: dynamical; systems; basis; vortex; interactions

The dynamical systems view of turbulence in fluid dynamics considers turbulent fluid flow as a trajectory in a very high-dimensional dynamical system. The trajectory shadows the unstable periodic orbits of this dynamical system closely. We aim to investigate these unstable periodic orbits, and compute any heteroclinic connections which exist between them, using new computational tools such as differentiable programming. It is also well known that any smoothly continuous solution of the Euler equation (the inviscid limit of the Navier-Stokes equations) can be obtained by taking the limit of suitable spatial distributions of point vortices. For this reason, we apply these new computational tools to the point vortex model, and discover a dense library of invariant solutions. We also aim to discover which, if any, of these invariant point vortex solutions are dynamically relevant in viscous turbulent flow.

流体动力学中紊流的动力系统观把紊流看作是一个非常高维动力系统中的轨迹。该轨迹与该动力系统的不稳定周期轨道密切相关。我们的目标是研究这些不稳定的周期轨道，并计算它们之间存在的任何异斜连接，使用新的计算工具，如可微规划。众所周知，欧拉方程（Navier-Stokes方程的无粘极限）的任何光滑连续解都可以通过取点涡的适当空间分布的极限而得到。因此，我们将这些新的计算工具应用于点涡模型，并发现了一个密集的不变解库。我们还旨在发现哪些，如果有的话，这些不变点涡解在粘性湍流中是动态相关的。