MLTURB: A new understanding of turbulence via a machine-learnt dynamical systems theory

MLTURB：通过机器学习动力系统理论对湍流的新理解

• 批准号: EP/Y004094/1
• 负责人: Jacob Page
• 金额: $ 153.7万
• 依托单位: University of Edinburgh
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2023
• 资助国家: 英国
• 起止时间: 2023 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FY004094%2F1
• 关键词: MLTURB; new; understanding; turbulence; via

Turbulence at very large scales is a complex, nonlinear problem of fundamental scientific andsocietal importance. Turbulent computations often rely on a "subgrid" model for the smaller,dissipative scales of motion. However, accurate simulation and prediction in the large-scale flowsof paramount industrial and geophysical importance requires a subgrid which covers a greaterrange of scales - and hence must encode more of the turbulent dynamics. There is, therefore, apressing need for answers to long-standing questions on the dynamics of energy transfermechanisms in strongly turbulent fluids. This proposal is focused on establishing this newunderstanding, focusing on both the dynamical processes at play in the turbulent energy cascadeand the rare, small-scale intermittent bursting events which are associated with extreme localvalues of drag or heat transfer. The new methodology is rooted in dynamical systems theory builtaround exact, unstable solutions of the governing equations. This approach has beentransformative in transitional/weakly turbulent flows, but has so far proved challenging to apply inparameter regimes of industrial relevance, due to the difficulties associated with identifying andconverging the unstable solutions. These limitations are overcome here via a new approach usingnovel machine learning algorithms and differentiable programming - with the necessary computepower and expertise provided through a collaboration with Google's Accelerated Sciences team.These tools are complemented by a robust low-order modelling framework based on the Koopmanoperator, which will be used both as both a tool to understand the dynamics encapsulated in theunstable solutions (and around them in phase space) and also to probe even more stronglyturbulent flows to establish the dominant mechanisms and assess exactly which dynamicalprocesses are required in the subgrid scale models of the future.

大尺度湍流是一个复杂的非线性问题，具有重要的科学和社会意义。湍流计算通常依赖于较小的耗散运动尺度的“子网格”模型。然而，在工业和地球物理上具有重要意义的大规模流动中，精确的模拟和预测需要一个覆盖更大范围尺度的子网格，因此必须编码更多的湍流动力学。因此，迫切需要回答关于强湍流流体中能量传递机制动力学的长期问题。本提案的重点是建立这种新的理解，关注在湍流能量级联中起作用的动力学过程和罕见的小规模间歇性爆炸事件，这些事件与极端的局部阻力或传热值有关。新方法植根于动力系统理论，建立在控制方程的精确、不稳定解的基础上。这种方法在过渡性/弱湍流中具有变革性，但由于与识别和收敛不稳定解相关的困难，到目前为止，在工业相关的参数体系中应用这种方法具有挑战性。通过与谷歌的加速科学团队合作，利用必要的计算机能力和专业知识，利用新颖的机器学习算法和可微分编程的新方法克服了这些限制。这些工具是由一个基于Koopmanoperator的强大的低阶建模框架补充的，它将被用作理解不稳定解决方案（以及在相空间中围绕它们）中包含的动力学的工具，也可以用来探测更强的湍流，以建立主导机制，并准确评估哪些动态过程是需要在未来的子网格尺度模型中。