剪切流动的空间模式稳定性问题特征值分布  

Eigenvalue spectra of spatial stability for shear flows

作　　者：王飞骏 武之峥 吕军波 张永明[1,3,4] 刘建华[5,6] WANG Feijun;WU Zhizheng;LV Junbo;ZHANG Yongming;LIU Jianhua(Department of Mechanics,Tianjin University,Tianjin 300072;School of Mechanical Engineering and Automation,Harbin Institute of Technology,Shenzhen 518055;Laboratory for High-Speed Aerodynamics,Tianjin University,Tianjin 300072;Tianjin Key Laboratory of Modern Engineering Mechanics,Tianjin 300072;China Ship Scientific Research Center,Wuxi 214082;Taihu Laboratory of Deepsea Technological Science,Wuxi 214082)

机构地区：[1]天津大学力学系,天津300072 [2]哈尔滨工业大学(深圳)机电工程与自动化学院,深圳518055 [3]天津大学高速空气动力学研究室,天津300072 [4]天津现代工程力学重点实验室,天津300072 [5]中国船舶科学研究中心,无锡214082 [6]深海技术科学太湖实验室,无锡214082

出　　处：《中国科学：物理学、力学、天文学》2024年第10期112-128,共17页Scientia Sinica Physica,Mechanica & Astronomica

基　　金：国家自然科学基金(编号:91952301,12072230)资助项目。

摘　　要：获得和充分了解剪切流动中的线性小扰动的特征值分布是流体力学中的重要问题.本文使用Arnoldi方法数值计算剪切流在空间模式下的线性稳定性方程的特征值分布及其特征函数.针对四种典型的不可压缩和可压缩剪切流动,本文得到了其在空间模式下的特征值分布,分析了其连续谱和离散谱的特征.此外,本文还得到并分析了各个分支谱的特征函数.结果表明,空间模式相较于时间模式,特征值分布更复杂,特征值的分支更多.For fluid dynamics,it is undoubtedly very important to obtain and achieve the insights into the eigenvalue spectra of disturbances of flow fields.In this paper,the Arnoldi method is employed to numerically solve the eigenvalue spectra and eigenfunction of the spatial linear stability equation for shear flows.Specifically,four classical compressible and incompressible shear flows are numerically treated.This work obtains the spectra of their eigenvalues in spatial stability,and then analyzes the characteristics of continuous and discrete spectra.In addition,the eigenfunctions of each branch spectrum are solved and analyzed.The results indicate that compared to the temporal mode,there are more complex spectra of eigenvalues and more spectral branches in the spatial mode.

关 键 词：特征值 空间模式 稳定性方程 Arnoldi方法 特征函数 

分 类 号：O35[理学—流体力学]