Wave interactions and fluid flows /
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| Author / Creator: | Craik, Alex D. D. |
|---|---|
| Imprint: | Cambridge [Cambridgeshire] ; New York : Cambridge University Press, 1985. |
| Description: | xii, 322 p. : ill. ; 24 cm. |
| Language: | English |
| Series: | Cambridge monographs on mechanics and applied mathematics |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/786418 |
Table of Contents:
- Preface
- 1. Introduction
- 1. Introduction
- 2. Linear wave interactions
- 2. Flows with piecewise-constant density and velocity
- 2.1. Stability of an interface
- 2.2. A three-layer model
- 2.3. An energy criterion
- 2.4. Viscous dissipation
- 3. Flows with constant density and continuous velocity profile
- 3.1. Stability of constant-density flows
- 3.2. Critical layers and wall layers
- 4. Flows with density stratification and piecewise-constant velocity
- 4.1. Continuously-stratified flows
- 4.2. Vortex sheet with stratification
- 4.3. Over-reflection and energy flux
- 4.4. The influence of boundaries
- 5. Flows with continuous profiles of density and velocity
- 5.1. Unbounded shear layers
- 5.2. Bounded shear layers
- 5.3. The critical layer in inviscid stratified flow
- 5.4. Diffusive effects
- 6. Models of mode coupling
- 6.1. Model dispersion relations
- 6.2. Mode conversion in inhomogeneous media
- 7. Eigenvalue spectra and localized disturbances
- 7.1. The temporal eigenvalue spectrum
- 7.2. The spatial eigenvalue spectrum
- 7.3. Evolution of localized disturbances
- 3. Introduction to nonlinear theory
- 8. Introduction to nonlinear theory
- 8.1. Introductory remarks
- 8.2. Description of a general disturbance
- 8.3. Review of special cases
- 4. Waves and mean flows
- 9. Spatially-periodic waves in channel flows
- 9.1. The mean-flow equations
- 9.2. Particular solutions
- 9.3. The viscous wall layer
- 10. Spatially-periodic waves on deformable boundaries
- 10.1. The Eulerian drift velocity of water waves
- 10.2. 'Swimming' of a wavy sheet
- 11. Modulated wave-packets
- 11.1. Waves in viscous channel flows
- 11.2. Waves on a free surface
- 11.3. Wave propagation in inhomogeneous media
- 11.4. Wave action and energy
- 11.5. Waves in inviscid stratified flow
- 11.6. Mean flow oscillations due to dissipation
- 12. Generalized Lagrangian mean (GLM) formulation
- 12.1. The GLM equations
- 12.2. Pseudomomentum and pseudoenergy
- 12.3. Surface gravity waves
- 12.4. Inviscid shear-flow instability
- 13. Spatially-periodic mean flows
- 13.1. Forced motions
- 13.2. Wave-driven longitudinal-vortex instability
- 5. Three-wave resonance
- 14. Conservative wave interactions
- 14.1. Conditions for resonance
- 14.2. Resonance of capillary-gravity waves
- 14.3. Some properties of the interaction equations
- 14.4. Wave-interaction experiments
- 15. Solutions of the conservative interaction equations
- 15.1. The one-dimensional solutions
- 15.2. Inverse-scattering solution in two dimensions
- 15.3. Solutions in three and four dimensions
- 15.4. Long wave--short wave interactions
- 16. Linearly damped waves
- 16.1. One wave heavily damped
- 16.2. Waves dependent on t only
- 16.3. Higher-order effects
- 17. Non-conservative wave interactions
- 17.1. Resonant triads in shear flows
- 17.2. The interaction equations
- 17.3. Some particular solutions
- 6. Evolution of a nonlinear wave-train
- 18. Heuristic derivation of the evolution equations
- 19. Weakly nonlinear waves in inviscid fluids
- 19.1. Surface and interfacial waves
- 19.2. Internal waves
- 19.3. Baroclinic waves
- 20. Weakly nonlinear waves in shear flows
- 20.1. Waves in inviscid shear flows
- 20.2. Near-critical plane Poiseuille flow
- 20.3. Non-critical (nearly) parallel flows
- 21. Properties of the evolution equations
- 21.1. Nonlinear Schrodinger equation with real coefficients
- 21.2. Davey--Stewartson equations with real coefficients
- 21.3. Nonlinear Schrodinger equation with complex coefficients
- 21.4. Korteweg--de Vries equation and its relatives
- 22. Waves of larger amplitude
- 22.1. Large-amplitude surface waves
- 22.2. Higher-order instability of wave-trains
- 22.3. Numerical work on shear-flow instability
- 22.4. The nonlinear critical layer
- 22.5. Taylor--Couette flow and Rayleigh-Benard convection
- 7. Cubic three- and four-wave interactions
- 23. Conservative four-wave interactions
- 23.1. The resonance condition
- 23.2. The temporal evolution equations
- 23.3. Properties of the evolution equations
- 23.4. Zakharov's equation for gravity waves
- 23.5. Properties of Zakharov's equation
- 24. Mode interactions in Taylor--Couette flow
- 24.1. Axisymmetric flow
- 24.2. Periodic wavy vortices
- 24.3. Effects of finite length
- 24.4. Doubly-periodic and 'chaotic' flow
- 25. Rayleigh--Benard convection
- 25.1. Introduction
- 25.2. Instabilities of rolls
- 25.3. Rolls in finite containers
- 25.4. Three-roll interactions
- 26. Wave interactions in planar shear flows
- 26.1. Three dominant waves
- 26.2. Analysis of four-wave interactions
- 26.3. Direct computational approach
- 8. Strong interactions, local instabilities and turbulence: a postscript
- 27. Strong interactions, local instabilities and turbulence: a postscript
- 27.1. Short waves and long waves
- 27.2. Local transition in shear flows
- 27.3. Some thoughts on transition and turbulence
- References
- Index
