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內容簡介

　　迴顧瞭過去10年在壁湍流和自由剪切流轉捩問題的數值研究中取得的重要進展，介紹瞭數值方法和模式研究方麵的進展，以及由此帶來的關於轉捩理論認識上的進展。對於壁麵流動，文中主要介紹瞭漸進穩定流動中"跨越(bypass)轉捩"研究中的各種觀點。本文也簡要介紹瞭對感受性和轉捩控製方麵的研究。

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目錄

1 Introduction and General Results1.1 Introduction1.2 Nonlinear Disturbance Equations1.3 Definition of Stability and Critical Reynolds Numbers1.3.1 Definition of Stability1.3.2 Critical Reynolds Numbers1.3.3 Spatial Evolution of Disturbances1.4 The Reynolds-Orr Equation1.4.1 Derivation of the Reynolds-Orr Equation1.4.2 The Need for Linear Growth Mechanisms
Ⅰ Temporal Stability of Parallel Shear Flows2 Linear Inviscid Analysis2.1 Inviscid Linear Stability Equations2.2 Modal Solutions2.2.1 General Results2.2.2 Dispersive Effects and Wave Packets2.3 Initial Value Problem2.3.1 The Inviscid Initial Value Problem2.3.2 Laplace Transform Solution2.3.3 Solutions to the Normal Vorticity Equation2.3.4 Example: Couette Flow2.3.5 Localized Disturbances3 Eigensolutions to the Viscous Problem3.1 Viscous Linear Stability Equations3.1.1 The Velocity-Vorticity Formulation3.1.2 The Orr-Sommerfeld and Squire Equations3.1.3 Squire's Transformation and Squire's Theorem3.1.4 Vector Modes3.1.5 Pipe Flow3.2 Spectra and Eigenfunctions3.2.1 Discrete Spectrum3.2.2 Neutral Curves3.2.3 Continuous Spectrum3.2.4 Asymptotic Results3.3 Further Results on Spectra and Eigenfunctions3.3.1 Adjoint Problem and Bi-Orthogonality Condition3.3.2 Sensitivity of Eigenvalues3.3.3 Pseudo-Eigenvalues3.3.4 Bounds on Eigenvalues3.3.5 Dispersive Effects and Wave Packets4 The Viscous Initial Value Problem4.1 The Viscous Initial Value Problem4.1.1 Motivation4.1.2 Derivation of the Disturbance Equations4.1.3 Disturbance Measure4.2 The Forced Squire Equation and Transient Growth4.2.1 Eigenfunction Expansion4.2.2 Blasius Boundary Layer Flow4.3 The Complete Solution to the Initial Value Problem4.3.1 Continuous Formulation4.3.2 Discrete Formulation4.4 Optimal Growth4.4.1 The Matrix Exponential4.4.2 Maximum Amplification4.4.3 Optimal Disturbances4.4.4 Reynolds Number Dependence of Optimal Growth4.5 Optimal Response and Optimal Growth Rate4.5.1 The Forced Problem and the Resolvent4.5.2 Maximum Growth Rate4.5.3 Response to Stochastic Excitation4.6 Estimates of Growth4.6.1 Bounds on Matrix Exponential……Ⅱ Stability of Complex Flows and TransitionⅢ Appendix

精彩書摘

　　1.1 Introduction　　Hydrodynamic stability theory is concerned with the response of a laminarflow to a disturbance of small or moderate amplitude. If the flow returns toits original laminar state one defines the flow as stable， whereas if the dis-turbance grows and causes the laminar flow to change into a different state，one defines the flow as unstable. Instabilities often result in turbulent fluidmotion， but they may also take the flow into a different laminar， usuallymore complicated state. Stability theory deals with the mathematical anal-ysis of the evolution of disturbances superposed on a laminar base flow. Inmany cases one assumes the disturbances to be small so that further sim-plifications can be justified. In particular， a linear equation governing theevolution of disturbances is desirable. As the disturbance velocities growabove a few percent of the base flow， nonlinear effects become importantand the linear equations no longer accurately predict the disturbance evo-lution. Although the linear equations have a limited region of validity theyare important in detecting physical growth mechanisms and identifyingdominant disturbance types.　　In this section we will derive the nonlinear equations governing the de-velopment of a disturbance on a laminar base flow， define various types ofstability， and discuss some general concepts and results.　　……

前言/序言

剪切流中的穩定性和轉捩 下載 mobi epub pdf txt 電子書

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