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