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由拟序结构控制。为了更好地理解它们的作用，近年来出现了一种复杂的方法--解决方案分析（RA）。RA的力量在于，它产生一组空间模式，直接从运动方程和平均流的知识中描述最重要的流结构，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和缺乏的权力，以解释如何在不同尺度的结构动态相互作用，这个项目的首要目标是开发一种方法，可以“关闭”一个基于RA的模型。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，从而提供一个时空湍流速度场，该速度场是合成生成的，而无需模拟。从计算的角度来看，这可以通过解决一个相当小的维度的优化问题，由于RA的压缩功率。该方法的潜力在于，它将使获得详细的洞察复杂的流动动力学更便宜比尺度解析模拟。反过来，这将促进和加速各种应用中的流动分析、参数探索和工程设计。本研究的具体目标是开发新的算法和计算工具，以适应这种模式，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/通道中的湍流以及海崖体和流线型体周围的分离流。

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.