Synthetic simulation of turbulent flow using resolvent analysis

在湍流中，具有重要实际意义的输运过程和平均流量主要受相干结构的支配。为了更好地了解它们的作用，近年来出现了一种复杂的方法--解决方案分析(RA)。RA的强大之处在于，它直接从运动方程和平均流知识中产生一组描述最重要流动结构的空间模式，而不需要昂贵的尺度分辨模拟或实验。然而，RA只描述了流体运动的运动学，缺乏解释不同尺度上的结构如何动态相互作用的能力。该项目的总体目标是开发一种能够“关闭”基于RA的模型的方法学。其基本思想是确定振幅系数来“权衡”不同结构的贡献，例如平衡动力学行为，从而提供一个在没有模拟的情况下综合产生的时空湍流速度场。从计算的角度来看，由于RA的压缩能力，这可以通过解决相当小的维度的优化问题来实现。这种方法的潜力在于，它将使人们能够以比尺度分辨模拟更低的成本获得对复杂流动动力学的详细了解。反过来，这将促进和加快各种应用中的流动分析、参数探索和工程设计。这项研究的具体目标是开发新的算法和计算工具来适应这一范式，并在各种实际感兴趣的三维流体系统中演示该方法，例如管道/通道中的湍流以及绕钝体和流线型物体的分离流动。

In turbulent flows, transport processes and average flow quantities of great practical relevance are dominated by coherent structures. In an effort to better understand their role, a sophisticated approach - Resolvent Analysis (RA) - has emerged in recent years. The power of RA is that it yields a set of spatial modes describing the most important flow structures directly from the equations of motion and from knowledge of the mean flow, without requiring expensive scale-resolving simulations or experiments. However, RA only describes the kinematics of fluid motion and lacks the power to explain how structures across different scales interact dynamically with each other.The overarching aim of this project is to develop a methodology that can "close" a RA-based model. The fundamental idea is to determine amplitude coefficients to "weigh" the contribution of different structures such as to balance dynamical behaviour, thus providing a space-time turbulent velocity field that has been generated synthetically, without simulation. From a computational standpoint, this can be achieved by solving an optimisation problem of rather small dimension, owing to the compressive power of RA. The potential of the approach is that it would enable obtaining detailed insight into the dynamics of complex flows more cheaply than with scale-resolving simulation. In turn, this would facilitate and accelerate flow analysis, parameter exploration and engineering design in a variety of applications. The specific objectives of this research are to develop new algorithms and computational tools to suit this paradigm and to demonstrate the method in a variety of three-dimensional fluid systems of practical interest, such as turbulent flows in pipes/channels and separated flows around bluff and streamlined bodies.