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.