Wave Interactions and Fluid Flows

Wave Interactions and Fluid Flows

Paperback Cambridge Monographs on Mechanics & Applied Mathematics

By (author) Alex D. D. Craik, Series edited by Mark J. Ablowitz, Series edited by S.H. Davis, Series edited by E. J. Hinch, Series edited by A. Iserles, Series edited by J. Ockendon, Series edited by P.J. Olver

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  • Publisher: CAMBRIDGE UNIVERSITY PRESS
  • Format: Paperback | 336 pages
  • Dimensions: 152mm x 226mm x 24mm | 522g
  • Publication date: 7 July 1988
  • Publication City/Country: Cambridge
  • ISBN 10: 0521368294
  • ISBN 13: 9780521368292
  • Edition statement: Reprint
  • Illustrations note: line drawings
  • Sales rank: 1,296,845

Product description

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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Review quote

'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

Table of contents

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.