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Wave Interactions and Fluid Flows : Cambridge Monographs on Mechanics & Applied Mathematics - Alex D. D. Craik

Wave Interactions and Fluid Flows

Cambridge Monographs on Mechanics & Applied Mathematics

Paperback Published: 5th September 1988
ISBN: 9780521368292
Number Of Pages: 336

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Wave Interactions and Fluid Flows is a coherent, up-to-date and comprehensive account of theory and experiment on wave-interaction phenomena, both in fluids at rest and in shear flows. On the one hand, this includes water waves, internal waves, their evolution and interaction and associated wave-driven mean flows; on the other, phenomena of nonlinear hydrodynamic stability, especially those leading to the onset of turbulence. Close similarities - and crucial differences - exist between these two classes of phenomena and their treatment in this single study provides a particularly valuable bridge between more specialised, but related, disciplines. As a result, this unique book will appeal to researchers and graduate students of fluid mechanics in its widest sense, including the study of wave-interaction phenomena in such diverse fields as meteorology, aeronautical and hydraulic engineering, optics, solar physics and population dynamics. Dr Craik is an active researcher of long-standing at the University of St Andrews and has wide experience in the field of fluid mechanics.

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'The theme that the author has adopted for his monograph, as reflected in its title, has enabled him to draw together, in a coherent and successful manner, a large amount of material that spans a range of, perhaps not obviously related, fluid-dynamical phenomena.' Contemporary Physics 'I enjoyed reading this book; the discussion of the topics that I am familiar with served as a refreshing, integrated review; the rest of the discussion outlines the important developments and gives enough references to get someone started who is seriously interested in exploring the subject in more detail.' Science

Prefacep. xi
Introductionp. 1
Introductionp. 1
Linear wave interactionsp. 10
Flows with piecewise-constant density and velocityp. 10
Stability of an interfacep. 10
A three-layer modelp. 14
An energy criterionp. 17
Viscous dissipationp. 19
Flows with constant density and continuous velocity profilep. 21
Stability of constant-density flowsp. 21
Critical layers and wall layersp. 23
Flows with density stratification and piecewise-constant velocityp. 27
Continuously-stratified flowsp. 27
Vortex sheet with stratificationp. 29
Over-reflection and energy fluxp. 31
The influence of boundariesp. 33
Flows with continuous profiles of density and velocityp. 35
Unbounded shear layersp. 35
Bounded shear layersp. 37
The critical layer in inviscid stratified flowp. 41
Diffusive effectsp. 44
Models of mode couplingp. 45
Model dispersion relationsp. 45
Mode conversion in inhomogeneous mediap. 49
Eigenvalue spectra and localized disturbancesp. 51
The temporal eigenvalue spectrump. 51
The spatial eigenvalue spectrump. 58
Evolution of localized disturbancesp. 59
Introduction to nonlinear theoryp. 65
Introduction to nonlinear theoryp. 65
Introductory remarksp. 65
Description of a general disturbancep. 66
Review of special casesp. 69
Waves and mean flowsp. 75
Spatially-periodic waves in channel flowsp. 75
The mean-flow equationsp. 75
Particular solutionsp. 77
The viscous wall layerp. 78
Spatially-periodic waves on deformable boundariesp. 81
The Eulerian drift velocity of water wavesp. 81
'Swimming' of a wavy sheetp. 84
Modulated wave-packetsp. 87
Waves in viscous channel flowsp. 87
Waves on a free surfacep. 90
Wave propagation in inhomogeneous mediap. 95
Wave action and energyp. 98
Waves in inviscid stratified flowp. 100
Mean flow oscillations due to dissipationp. 104
Generalized Lagrangian mean (GLM) formulationp. 105
The GLM equationsp. 105
Pseudomomentum and pseudoenergyp. 108
Surface gravity wavesp. 109
Inviscid shear-flow instabilityp. 111
Spatially-periodic mean flowsp. 113
Forced motionsp. 113
Wave-driven longitudinal-vortex instabilityp. 120
Three-wave resonancep. 123
Conservative wave interactionsp. 123
Conditions for resonancep. 123
Resonance of capillary-gravity wavesp. 125
Some properties of the interaction equationsp. 129
Wave-interaction experimentsp. 132
Solutions of the conservative interaction equationsp. 136
The one-dimensional solutionsp. 136
Inverse-scattering solution in two dimensionsp. 139
Solutions in three and four dimensionsp. 147
Long wave--short wave interactionsp. 150
Linearly damped wavesp. 151
One wave heavily dampedp. 151
Waves dependent on t onlyp. 152
Higher-order effectsp. 159
Non-conservative wave interactionsp. 161
Resonant triads in shear flowsp. 161
The interaction equationsp. 166
Some particular solutionsp. 170
Evolution of a nonlinear wave-trainp. 172
Heuristic derivation of the evolution equationsp. 172
Weakly nonlinear waves in inviscid fluidsp. 176
Surface and interfacial wavesp. 176
Internal wavesp. 182
Baroclinic wavesp. 184
Weakly nonlinear waves in shear flowsp. 188
Waves in inviscid shear flowsp. 188
Near-critical plane Poiseuille flowp. 190
Non-critical (nearly) parallel flowsp. 193
Properties of the evolution equationsp. 199
Nonlinear Schrodinger equation with real coefficientsp. 199
Davey--Stewartson equations with real coefficientsp. 204
Nonlinear Schrodinger equation with complex coefficientsp. 206
Korteweg--de Vries equation and its relativesp. 209
Waves of larger amplitudep. 212
Large-amplitude surface wavesp. 212
Higher-order instability of wave-trainsp. 215
Numerical work on shear-flow instabilityp. 219
The nonlinear critical layerp. 226
Taylor--Couette flow and Rayleigh-Benard convectionp. 229
Cubic three- and four-wave interactionsp. 231
Conservative four-wave interactionsp. 231
The resonance conditionp. 231
The temporal evolution equationsp. 233
Properties of the evolution equationsp. 235
Zakharov's equation for gravity wavesp. 237
Properties of Zakharov's equationp. 241
Mode interactions in Taylor--Couette flowp. 244
Axisymmetric flowp. 244
Periodic wavy vorticesp. 246
Effects of finite lengthp. 249
Doubly-periodic and 'chaotic' flowp. 253
Rayleigh--Benard convectionp. 258
Introductionp. 258
Instabilities of rollsp. 259
Rolls in finite containersp. 264
Three-roll interactionsp. 268
Wave interactions in planar shear flowsp. 272
Three dominant wavesp. 272
Analysis of four-wave interactionsp. 275
Direct computational approachp. 279
Strong interactions, local instabilities and turbulence: a postscriptp. 282
Strong interactions, local instabilities and turbulence: a postscriptp. 282
Short waves and long wavesp. 282
Local transition in shear flowsp. 283
Some thoughts on transition and turbulencep. 286
Referencesp. 289
Indexp. 319
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780521368292
ISBN-10: 0521368294
Series: Cambridge Monographs on Mechanics & Applied Mathematics
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 336
Published: 5th September 1988
Publisher: CAMBRIDGE UNIV PR
Country of Publication: GB
Dimensions (cm): 22.96 x 15.37  x 2.13
Weight (kg): 0.52

Earn 151 Qantas Points
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