Physics of Transitional Shear Flows Instability and Laminar–Turbulent Transition in Incompressible Near-Wall Shear Layers /
Starting from fundamentals of classical stability theory, an overview is given of the transition phenomena in subsonic, wall-bounded shear flows. At first, the consideration focuses on elementary small-amplitude velocity perturbations of laminar shear layers, i.e. instability waves, in the simplest...
| Main Authors: | , , , |
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| Corporate Author: | |
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Dordrecht :
Springer Netherlands,
2012.
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| Series: | Fluid Mechanics and Its Applications,
98 |
| Subjects: | |
| Online Access: | Full Text via HEAL-Link |
Table of Contents:
- Part I Fundamentals of the linear stability theory : 1 Concept of hydrodynamic stability
- 1.1 Hydrodynamic stability
- 1.2 Stability of fluid motion in time
- 1.2.1 Critical parameters for onset of instability
- 1.2.2 Conditional stability
- 1.2.3 Growth of disturbance energy
- References
- Further Reading
- 2 Theoretical aspects : 2.1 Formulation of linear hydrodynamic stability problems
- 2.1.1 Spectral formulation of stability
- 2.1.2 Inviscid instability mechanism
- 2.1.3 Viscous instability mechanism
- 2.2 Instability in space
- 2.3 Gaster’s transformation
- 2.4 Squire theorem
- 2.5 Adjoint problem and bi-orthogonality of normal modes
- 2.6 Completeness of solutions for the Orr–Sommerfeld and Squire equations
- References
- Further Reading
- Part II Generic problems : 3 Instability of plane parallel flows : 3.1 Plane Couette flow
- 3.2 Plane Poiseuille flow
- 3.2.1 Numerical results
- 3.2.2 Experimental linear stability investigations
- 3.3 Method of linear stability calculations
- Exercises
- References
- Further Reading
- 4 Instability of the flat-plate boundary layer : 4.1 Historical notes
- 4.2 Solution of the Orr–Sommerfeld equation for the boundary layers
- 4.3 Nonparallel flow effects
- 4.3.1 Outline of theoretical approaches to account for nonparallel effects
- 4.3.2 Modern view on the place and role of nonparallel effects in the Blasius boundary layer
- Exercises
- References
- Further Reading
- 5 Instabilities of plane flows over curvilinear surfaces: 5.1 Influence of curvature on the basic flow
- 5.1.1 Equations of motion in cylindrical coordinates
- 5.1.2 Description of the flow in boundary layers over curvilinear surfaces
- 5.2 Hydrodynamic instability at curvilinear surfaces
- 5.2.1 Taylor problem
- 5.2.2 Dean problem
- 5.2.3 G¨ortler problem
- Exercises
- References
- Further Reading
- 6 Some other basic factors of shear-layer stability: 6.1 Axial flow symmetry
- 6.2 Two-dimensional geometry
- 6.3 Transverse flow periodicity
- 6.4 Pressure gradients
- 6.4.1 Streamwise pressure gradient
- 6.4.2 Transverse pressure gradient
- 6.5 Heat transfer
- 6.6 Fluid suction
- 6.7 Compliant boundaries
- 6.8 Dusty flow
- Exercises
- References
- Further Reading
- 7 Instability of separated boundary layers
- 7.1 Basic features of separated flow instability
- 7.2 Linear instability at flow separation in plane configurations
- 7.2.1 Waveform
- 7.2.2 Growth rates
- 7.2.3 Propagation velocities
- 7.3 Instability of axisymmetric separation bubbles
- 7.4 Flow instability at separation of a swept-wing boundary layer
- 7.5 Outline of approaches for linear stability calculations in separation regions
- Exercises
- References
- Further Reading
- Part III Special topics on linear stability
- 8 Linear wave packets of instability waves
- 8.1 Classification of wave packets
- 8.2 Group velocity
- 8.3 Experimental investigations of wave packets
- Exercises
- References
- Further Reading
- 9 Transient disturbances in shear flows
- 9.1 Lift-up effect
- 9.2 Growth of optimal disturbances
- 9.3 Experimental studies
- Exercises
- References
- Further Reading
- 10 Excitation of shear flow disturbances
- 10.1 Receptivity problem
- 10.2 Localized and distributed generation of laminar flow disturbances
- 10.3 Methodology of receptivity studies
- 10.3.1 Theoretical approaches
- 10.3.2 Experimental strategy
- 10.4 Receptivity of two-dimensional boundary layers
- 10.4.1 Leading-edge receptivity
- 10.4.2 Excitation of instability waves at local boundary-layer nonuniformities
- 10.4.3 Receptivity to localized unsteady disturbances
- 10.4.4 Excitation of instability waves at laminar boundary-layer separation
- 10.5 Receptivity of a swept-wing boundary layer
- 10.6 Excitation of the G¨ortler vortices
- 10.7 Excitation of streaky structures
- 10.7.1 Localized generation of streaks
- 10.7.2 Distributed generation of streaks
- References
- Further Reading
- 11 Secondary instabilities of shear layers
- 11.1 Secondary instability in a flow modulated by the Tollmien–Schlichting waves
- 11.2 Secondary instability in flows modulated by streamwise vortices and streaks
- 11.3 Local high-frequency secondary instability
- References
- Further Reading
- Part IV Onset of turbulence
- 12 Nonlinear effects during the laminar–turbulent transition
- 12.1 Onset of nonlinearity
- 12.2 Basic nonlinear scenarios
- 12.2.1 K- and N-regimes of the laminar–turbulent transition
- 12.2.2 Oblique breakdown
- 12.2.3 Nonlinearity of locally separating boundary layers
- 12.3 Transition to turbulence in boundary layers at a high free-stream disturbance level
- 12.3.1 Linear Tollmien–Schlichting waves in the presence of streaks
- 12.3.2 Interaction of the streaks with the Tollmien–Schlichtingwaves
- References
- Further Reading
- 13 Generation of turbulence
- 13.1 Wave combinations and intermittency
- 13.2 Turbulent spots
- 13.2.1 Isolated turbulent spots
- 13.2.2 Interaction of turbulent spots
- 13.2.3 Turbulent spots in the presence of other disturbances
- 13.3 Super-late stage of the transition: ‘Deterministic turbulence’
- References
- Further Reading
- A Basic engineering aspects of the laminar–turbulent transition
- A.1 Transition prediction
- A.2 Outline of the linear control theory ;References
- Further Reading
- Index.
