An invitation to resolvent analysis

IF 2.2 3区工程技术 Q2 MECHANICS

Theoretical and Computational Fluid Dynamics Pub Date : 2024-08-19 DOI:10.1007/s00162-024-00717-x

Laura Victoria Rolandi, Jean Hélder Marques Ribeiro, Chi-An Yeh, Kunihiko Taira

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Abstract

Resolvent analysis is a powerful tool that can reveal the linear amplification mechanisms between the forcing inputs and the response outputs about a base flow. These mechanisms can be revealed in terms of a pair of forcing and response modes and the associated energy gains (amplification magnitude) at a given frequency. The linear relationship that ties the forcing and the response is represented through the resolvent operator (transfer function), which is constructed through spatially discretizing the linearized Navier–Stokes operator. One of the unique strengths of resolvent analysis is its ability to analyze statistically stationary turbulent flows. In light of the increasing interest in using resolvent analysis to study a variety of flows, we offer this guide in hopes of removing the hurdle for students and researchers to initiate the development of a resolvent analysis code and its applications to their problems of interest. To achieve this goal, we discuss various aspects of resolvent analysis and its role in identifying dominant flow structures about the base flow. The discussion in this paper revolves around the compressible Navier–Stokes equations in the most general manner. We cover essential considerations ranging from selecting the base flow and appropriate energy norms to the intricacies of constructing the linear operator and performing eigenvalue and singular value decompositions. Throughout the paper, we offer details and know-how that may not be available to readers in a collective manner elsewhere. Towards the end of this paper, examples are offered to demonstrate the practical applicability of resolvent analysis, aiming to guide readers through its implementation and inspire further extensions. We invite readers to consider resolvent analysis as a companion for their research endeavors.

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解析邀请函

残差分析是一种功能强大的工具，可以揭示基流的强迫输入和响应输出之间的线性放大机制。这些机制可以通过一对作用力和响应模式以及给定频率下的相关能量增益（放大倍数）来揭示。通过对线性化的纳维-斯托克斯算子进行空间离散化处理，可以用解析算子（传递函数）来表示约束和响应之间的线性关系。解析分析的独特优势之一是能够分析统计静止湍流。鉴于越来越多的人对使用旋转分析来研究各种流动感兴趣，我们提供了这本指南，希望能为学生和研究人员消除障碍，帮助他们开始开发旋转分析代码并将其应用于他们感兴趣的问题。为了实现这一目标，我们讨论了解析量分析的各个方面及其在识别基流主导流结构中的作用。本文的讨论以最一般的方式围绕可压缩 Navier-Stokes 方程展开。我们涵盖了从选择基流和适当的能量规范到构建线性算子和执行特征值和奇异值分解的复杂性等基本考虑因素。在整篇论文中，我们提供了读者可能无法在其他地方以集体方式获得的细节和诀窍。在本文末尾，我们还提供了一些实例来演示分解分析的实际应用性，旨在引导读者了解其实现方法，并启发读者进一步扩展。我们邀请读者考虑将 resolvent 分析作为其研究工作的辅助工具。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Theoretical and Computational Fluid Dynamics 物理-力学

CiteScore

5.80

自引率

2.90%

发文量

审稿时长

>12 weeks

期刊介绍： Theoretical and Computational Fluid Dynamics provides a forum for the cross fertilization of ideas, tools and techniques across all disciplines in which fluid flow plays a role. The focus is on aspects of fluid dynamics where theory and computation are used to provide insights and data upon which solid physical understanding is revealed. We seek research papers, invited review articles, brief communications, letters and comments addressing flow phenomena of relevance to aeronautical, geophysical, environmental, material, mechanical and life sciences. Papers of a purely algorithmic, experimental or engineering application nature, and papers without significant new physical insights, are outside the scope of this journal. For computational work, authors are responsible for ensuring that any artifacts of discretization and/or implementation are sufficiently controlled such that the numerical results unambiguously support the conclusions drawn. Where appropriate, and to the extent possible, such papers should either include or reference supporting documentation in the form of verification and validation studies.