剪切流中的稳定性和转捩 英文影印版
作者：斯科姆，DanS.Henningson 著
出版时间： 2014年版
内容简介
回顾了过去10年在壁湍流和自由剪切流转捩问题的数值研究中取得的重要进展，介绍了数值方法和模式研究方面的进展，以及由此带来的关于转捩理论认识上的进展。对于壁面流动，文中主要介绍了渐进稳定流动中"跨越(bypass)转捩"研究中的各种观点。本文也简要介绍了对感受性和转捩控制方面的研究。
目录
1 Introduction and General Results
1.1 Introduction
1.2 Nonlinear Disturbance Equations
1.3 Definition of Stability and Critical Reynolds Numbers
1.3.1 Definition of Stability
1.3.2 Critical Reynolds Numbers
1.3.3 Spatial Evolution of Disturbances
1.4 The Reynolds-Orr Equation
1.4.1 Derivation of the Reynolds-Orr Equation
1.4.2 The Need for Linear Growth Mechanisms
Ⅰ Temporal Stability of Parallel Shear Flows
2 Linear Inviscid Analysis
2.1 Inviscid Linear Stability Equations
2.2 Modal Solutions
2.2.1 General Results
2.2.2 Dispersive Effects and Wave Packets
2.3 Initial Value Problem
2.3.1 The Inviscid Initial Value Problem
2.3.2 Laplace Transform Solution
2.3.3 Solutions to the Normal Vorticity Equation
2.3.4 Example: Couette Flow
2.3.5 Localized Disturbances
3 Eigensolutions to the Viscous Problem
3.1 Viscous Linear Stability Equations
3.1.1 The Velocity-Vorticity Formulation
3.1.2 The Orr-Sommerfeld and Squire Equations
3.1.3 Squire's Transformation and Squire's Theorem
3.1.4 Vector Modes
3.1.5 Pipe Flow
3.2 Spectra and Eigenfunctions
3.2.1 Discrete Spectrum
3.2.2 Neutral Curves
3.2.3 Continuous Spectrum
3.2.4 Asymptotic Results
3.3 Further Results on Spectra and Eigenfunctions
3.3.1 Adjoint Problem and Bi-Orthogonality Condition
3.3.2 Sensitivity of Eigenvalues
3.3.3 Pseudo-Eigenvalues
3.3.4 Bounds on Eigenvalues
3.3.5 Dispersive Effects and Wave Packets
4 The Viscous Initial Value Problem
4.1 The Viscous Initial Value Problem
4.1.1 Motivation
4.1.2 Derivation of the Disturbance Equations
4.1.3 Disturbance Measure
4.2 The Forced Squire Equation and Transient Growth
4.2.1 Eigenfunction Expansion
4.2.2 Blasius Boundary Layer Flow
4.3 The Complete Solution to the Initial Value Problem
4.3.1 Continuous Formulation
4.3.2 Discrete Formulation
4.4 Optimal Growth
4.4.1 The Matrix Exponential
4.4.2 Maximum Amplification
4.4.3 Optimal Disturbances
4.4.4 Reynolds Number Dependence of Optimal Growth
4.5 Optimal Response and Optimal Growth Rate
4.5.1 The Forced Problem and the Resolvent
4.5.2 Maximum Growth Rate
4.5.3 Response to Stochastic Excitation
4.6 Estimates of Growth
4.6.1 Bounds on Matrix Exponential
……
Ⅱ Stability of Complex Flows and Transition
Ⅲ Appendix
