Fluid Dynamics: Part 4: Hydrodynamic Stability Theory

✍ Scribed by Anatoly Ruban, Jitesh Gajjar, Andrew Walton

• Publisher: Oxford University Press
• Year: 2023
• Tongue: English
• Leaves: 369
• Category: Library

✦ Table of Contents

Cover
titlepage
copyright
dedication
Preface
Contents
Introduction
Classical Hydrodynamic Stability Theory
1.1 Linear Stability Theory
1.1.1 Global stability analysis
1.2 Stability of Parallel Flows
1.2.1 Poiseuille flow
1.2.2 Analysis of two-dimensional perturbations
1.3 Stability of Boundary Layers
1.3.1 Basic flow
1.3.2 The parallel flow approximation
1.3.3 Stability analysis
1.3.4 Temporal and spatial instabilities
1.4 Inviscid Stability Theory
1.4.1 Properties of the Rayleigh equation
1.4.2 Inviscid instability of a laminar jet
1.5 Kelvin–Helmholtz Instability
1.6 Cross-Flow Vortices
1.6.1 Basic flow
1.6.2 Linear stability analysis
1.7 Centrifugal Instability
1.7.1 Taylor vortices
1.7.2 G¨ortler vortices
High-Reynolds-Number Analysis of Parallel and Shear Flow Instabilities
2.1 Problem Formulation
2.2 Asymptotic Analysis of the Orr–Sommerfeld Equation for Blasius Flow
2.2.1 Outer region
2.2.2 Main part of the boundary layer
2.3 Critical Layer and Stokes Layer Coincident: Lower Branch
2.3.1 The viscous sublayer
2.3.2 Canonical form of the dispersion equation
2.3.3 Numerical solution of the dispersion equation
2.4 Critical Layer and Stokes Layer Distinct: Upper Branch
2.4.1 Contribution of the critical layer
2.4.2 Analysis of the Stokes layer
2.4.3 The dispersion relations for the upper branch
2.5 Asymptotic Analysis of the Orr–Sommerfeld Equation for Plane Poiseuille Flow
2.5.1 Derivation of the lower branch eigenrelation
2.5.2 Derivation of the upper branch eigenrelation
2.6 Critical Layer Theory
2.6.1 Linear critical layer theory
2.6.2 Nonlinear critical layer theory
Boundary-Layer Receptivity
3.1 Terent’ev’s Problem
3.1.1 Problem formulation
3.1.2 Boundary layer before the vibrating ribbon
3.1.3 Triple-deck region
3.1.4 Viscous-inviscid interaction problem
3.1.5 Linear problem
3.1.6 Receptivity coefficient
3.2 Initial-Value Problem
3.2.1 Problem formulation
3.2.2 Numerical solution of the linear problem
3.2.3 Analysis of the wave packet
3.2.4 Convective and absolute instabilities
3.2.5 Centre of the wave packet
3.3 Generation of Tollmien–Schlichting Waves by Sound
3.3.1 Problem formulation
3.3.2 Unperturbed flow
3.3.3 Acoustic noise
3.3.4 Triple-deck region
3.3.5 Viscous-inviscid interaction problem
3.3.6 Linear receptivity
3.3.7 Receptivity coefficient
3.4 Further Advances in Receptivity Theory
Weakly Nonlinear Stability Theory
4.1 Landau’s Concept of Laminar-Turbulent Transition
4.2 Landau–Stuart Equation
4.2.1 Problem formulation
4.2.2 Asymptotic procedure
4.2.3 Linear perturbations
4.2.4 Quadratic approximation
4.2.5 Cubic approximation
4.2.6 Properties of the Landau–Stuart equation
4.3 Finite-Amplitude Nonlinear Travelling Wave Solutions
Coherent Structures and Self-Sustaining Processes in Shear Flows
5.1 The Fundamental Building Blocks of a Self-Sustaining Process
5.2 The Self-Sustaining Process (SSP) at Finite Reynolds Number
5.2.1 The roll flow
5.2.2 The streamwise streak
5.2.3 The three-dimensional travelling wave
5.2.4 The nonlinear feedback on the rolls
5.2.5 Full numerical solutions for plane Couette flow
5.3 Self-Sustaining Processes at High Reynolds Number: Vortex-Inviscid Wave Interaction
5.3.1 The core flow
5.3.2 Asymptotic behaviour near the critical curve
5.3.3 Inside the critical layer
5.4 Self-Sustaining Processes at High Reynolds Number: Vortex-Viscous Wave Interaction
5.4.1 The unforced roll/streak flow
5.4.2 The viscous wall layers
5.4.3 Wave feedback on the roll/streak core flow
5.4.4 Solution for small amplitude: weakly nonlinear theory
5.4.5 Full solution of the nonlinear interaction equations
5.5 More Recent Developments
References
Index
Figure Acknowledgements
Fig. I. 1:
Fig. I. 2:
Fig. I.4:
Fig. 1.23:
11,
Fig. 1.25:
Fig. 1.27:
Fig. 1.33:
17,
Fig. 1.38:
Fig. 4.6:
Fig. 5.1a:
30,
Fig. 5.1b:
Fig. 5.2:
287,
Fig. 5.11:
Fig. 5.12:
752,
Fig. 5.16: