Wave Interactions and Fluid Flows

Part I. Introduction: 1. Introduction; Part II. Linear Wave Interactions: 2. Flows with piecewise-constant density and velocity; 3. Flows with constant density and continuous velocity profile; 4. Flows with density stratification and piecewise-constant velocity; 5. Flows with continuous profiles of density and velocity; 6. Models of mode coupling; 7. Eigenvalue spectra and localized disturbances; Part III. Introduction to Nonlinear Theory: 8. Introduction to nonlinear theory; Part IV. Waves and Mean Flows: 9. Spatially-periodic waves in channel flows; 10. Spatially-periodic waves on deformable boundaries; 11. Modulated wave-packets; 12. Generalized Lagrangian mean (GLM) formulation; 13. Spatially-periodic means flows; Part V. Three-wave Resonance: 14. Conservative wave interactions; 15. Solutions of the conservative interaction equations; 16. Linearly damped waves; 17. Non-conservative wave interactions; Part VI. Evolution of a Nonlinear Wave-Train: 18. Heuristic derivation of the evolution equations; 19. Weakly nonlinear waves in inviscid fluids; 20. Weakly nonlinear waves in shear flows; 21. Properties of the evolution equations; 22. Waves of larger amplitude; Part VII. Cubic Three- and Four-wave Interactions: 23. Conservative four-wave interactions; 24. Mode interactions in Taylor-Couette flow; 25. Rayleigh-Benard convection; 26. Wave interactions in planar shear flows; Part VIII. Strong Interactions, Local Instabilities and Turbulence: A Postscript: 27. Strong interactions, local instabilities and turbulence: A postscript; References; Index.