| Preface | p. xi |
| Introduction | p. 1 |
| Introduction | p. 1 |
| Linear wave interactions | p. 10 |
| Flows with piecewise-constant density and velocity | p. 10 |
| Stability of an interface | p. 10 |
| A three-layer model | p. 14 |
| An energy criterion | p. 17 |
| Viscous dissipation | p. 19 |
| Flows with constant density and continuous velocity profile | p. 21 |
| Stability of constant-density flows | p. 21 |
| Critical layers and wall layers | p. 23 |
| Flows with density stratification and piecewise-constant velocity | p. 27 |
| Continuously-stratified flows | p. 27 |
| Vortex sheet with stratification | p. 29 |
| Over-reflection and energy flux | p. 31 |
| The influence of boundaries | p. 33 |
| Flows with continuous profiles of density and velocity | p. 35 |
| Unbounded shear layers | p. 35 |
| Bounded shear layers | p. 37 |
| The critical layer in inviscid stratified flow | p. 41 |
| Diffusive effects | p. 44 |
| Models of mode coupling | p. 45 |
| Model dispersion relations | p. 45 |
| Mode conversion in inhomogeneous media | p. 49 |
| Eigenvalue spectra and localized disturbances | p. 51 |
| The temporal eigenvalue spectrum | p. 51 |
| The spatial eigenvalue spectrum | p. 58 |
| Evolution of localized disturbances | p. 59 |
| Introduction to nonlinear theory | p. 65 |
| Introduction to nonlinear theory | p. 65 |
| Introductory remarks | p. 65 |
| Description of a general disturbance | p. 66 |
| Review of special cases | p. 69 |
| Waves and mean flows | p. 75 |
| Spatially-periodic waves in channel flows | p. 75 |
| The mean-flow equations | p. 75 |
| Particular solutions | p. 77 |
| The viscous wall layer | p. 78 |
| Spatially-periodic waves on deformable boundaries | p. 81 |
| The Eulerian drift velocity of water waves | p. 81 |
| 'Swimming' of a wavy sheet | p. 84 |
| Modulated wave-packets | p. 87 |
| Waves in viscous channel flows | p. 87 |
| Waves on a free surface | p. 90 |
| Wave propagation in inhomogeneous media | p. 95 |
| Wave action and energy | p. 98 |
| Waves in inviscid stratified flow | p. 100 |
| Mean flow oscillations due to dissipation | p. 104 |
| Generalized Lagrangian mean (GLM) formulation | p. 105 |
| The GLM equations | p. 105 |
| Pseudomomentum and pseudoenergy | p. 108 |
| Surface gravity waves | p. 109 |
| Inviscid shear-flow instability | p. 111 |
| Spatially-periodic mean flows | p. 113 |
| Forced motions | p. 113 |
| Wave-driven longitudinal-vortex instability | p. 120 |
| Three-wave resonance | p. 123 |
| Conservative wave interactions | p. 123 |
| Conditions for resonance | p. 123 |
| Resonance of capillary-gravity waves | p. 125 |
| Some properties of the interaction equations | p. 129 |
| Wave-interaction experiments | p. 132 |
| Solutions of the conservative interaction equations | p. 136 |
| The one-dimensional solutions | p. 136 |
| Inverse-scattering solution in two dimensions | p. 139 |
| Solutions in three and four dimensions | p. 147 |
| Long wave--short wave interactions | p. 150 |
| Linearly damped waves | p. 151 |
| One wave heavily damped | p. 151 |
| Waves dependent on t only | p. 152 |
| Higher-order effects | p. 159 |
| Non-conservative wave interactions | p. 161 |
| Resonant triads in shear flows | p. 161 |
| The interaction equations | p. 166 |
| Some particular solutions | p. 170 |
| Evolution of a nonlinear wave-train | p. 172 |
| Heuristic derivation of the evolution equations | p. 172 |
| Weakly nonlinear waves in inviscid fluids | p. 176 |
| Surface and interfacial waves | p. 176 |
| Internal waves | p. 182 |
| Baroclinic waves | p. 184 |
| Weakly nonlinear waves in shear flows | p. 188 |
| Waves in inviscid shear flows | p. 188 |
| Near-critical plane Poiseuille flow | p. 190 |
| Non-critical (nearly) parallel flows | p. 193 |
| Properties of the evolution equations | p. 199 |
| Nonlinear Schrodinger equation with real coefficients | p. 199 |
| Davey--Stewartson equations with real coefficients | p. 204 |
| Nonlinear Schrodinger equation with complex coefficients | p. 206 |
| Korteweg--de Vries equation and its relatives | p. 209 |
| Waves of larger amplitude | p. 212 |
| Large-amplitude surface waves | p. 212 |
| Higher-order instability of wave-trains | p. 215 |
| Numerical work on shear-flow instability | p. 219 |
| The nonlinear critical layer | p. 226 |
| Taylor--Couette flow and Rayleigh-Benard convection | p. 229 |
| Cubic three- and four-wave interactions | p. 231 |
| Conservative four-wave interactions | p. 231 |
| The resonance condition | p. 231 |
| The temporal evolution equations | p. 233 |
| Properties of the evolution equations | p. 235 |
| Zakharov's equation for gravity waves | p. 237 |
| Properties of Zakharov's equation | p. 241 |
| Mode interactions in Taylor--Couette flow | p. 244 |
| Axisymmetric flow | p. 244 |
| Periodic wavy vortices | p. 246 |
| Effects of finite length | p. 249 |
| Doubly-periodic and 'chaotic' flow | p. 253 |
| Rayleigh--Benard convection | p. 258 |
| Introduction | p. 258 |
| Instabilities of rolls | p. 259 |
| Rolls in finite containers | p. 264 |
| Three-roll interactions | p. 268 |
| Wave interactions in planar shear flows | p. 272 |
| Three dominant waves | p. 272 |
| Analysis of four-wave interactions | p. 275 |
| Direct computational approach | p. 279 |
| Strong interactions, local instabilities and turbulence: a postscript | p. 282 |
| Strong interactions, local instabilities and turbulence: a postscript | p. 282 |
| Short waves and long waves | p. 282 |
| Local transition in shear flows | p. 283 |
| Some thoughts on transition and turbulence | p. 286 |
| References | p. 289 |
| Index | p. 319 |
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