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Waves and Mean Flows, Second Edition

Book Description

Interactions between waves and mean flows play a crucial role in understanding the long-term aspects of atmospheric and oceanographic modelling. Indeed, our ability to predict climate change hinges on our ability to model waves accurately. This book gives a modern account of the nonlinear interactions between waves and mean flows, such as shear flows and vortices. A detailed account of the theory of linear dispersive waves in moving media is followed by a thorough introduction to classical wave-mean interaction theory. The author then extends the scope of the classical theory and lifts its restriction to zonally symmetric mean flows. It can be used as a fundamental reference, a course text, or by geophysicists and physicists needing a first introduction. This second edition includes brand new material, including a section on Langmuir circulations and the Craik–Leibovich instability. The author has also added exercises to aid students' learning.

Table of Contents

  1. Cover
  2. Half Title
  3. Series
  4. Title
  5. Copyright
  6. Epigraph
  7. Contents
  8. Preface
  9. PART ONE FLUID DYNAMICS AND WAVES
    1. 1 Elements of fluid dynamics
      1. 1.1 Flow kinematics
      2. 1.2 Perfect fluid dynamics
      3. 1.3 Conservation laws and energy
      4. 1.4 Circulation and vorticity
      5. 1.5 Rotating frames of reference
      6. 1.6 Shallow-water system
      7. 1.7 Notes on the literature
    2. 2 Linear waves
      1. 2.1 Linear dynamics
      2. 2.2 Notes on the literature
      3. 2.3 Exercises
    3. 3 Geometric wave theory
      1. 3.1 Two-dimensional refraction
      2. 3.2 Caustics
      3. 3.3 Notes on the literature
      4. 3.4 Exercises
    4. 4 Dispersive waves and ray tracing
      1. 4.1 Facets of group velocity
      2. 4.2 Examples of dispersive waves
      3. 4.3 Ray tracing for dispersive wavetrains
      4. 4.4 Ray tracing in moving media
      5. 4.5 Wave activity conservation laws
      6. 4.6 Notes on the literature
      7. 4.7 Exercises
  10. PART TWO WAVE–MEAN INTERACTION THEORY
    1. 5 Zonally symmetric wave–mean interaction theory
      1. 5.1 Basic assumptions
    2. 6 Internal gravity waves
      1. 6.1 Boussinesq system and stable stratification
      2. 6.2 Linear Boussinesq dynamics
      3. 6.3 Zonal pseudomomentum of internal waves
      4. 6.4 Mountain lee waves and drag force
      5. 6.5 Mean-flow response
      6. 6.6 Wave dissipation
      7. 6.7 Extension to variable stratification and density
      8. 6.8 Notes on the literature
      9. 6.9 Exercises
    3. 7 Shear flows
      1. 7.1 Linear Boussinesq dynamics with shear
      2. 7.2 Critical layers
      3. 7.3 Joint evolution of waves and the mean shear flow
      4. 7.4 Notes on the literature
      5. 7.5 Exercises
    4. 8 Three-dimensional rotating flow
      1. 8.1 Rotating Boussinesq equations on an f-plane
      2. 8.2 Linear structure
      3. 8.3 Mean-flow response and the vortical mode
      4. 8.4 Rotating vertical slice model
      5. 8.5 Notes on the literature
      6. 8.6 Exercises
    5. 9 Rossby waves and balanced dynamics
      1. 9.1 Quasi-geostrophic dynamics
      2. 9.2 Small amplitude wave–mean interactions
      3. 9.3 Rossby waves and turbulence
      4. 9.4 Notes on the literature
      5. 9.5 Exercises
    6. 10 Lagrangian-mean theory
      1. 10.1 Lagrangian and Eulerian averaging
      2. 10.2 Elements of GLM theory
      3. 10.3 Wave activity conservation in GLM theory
      4. 10.4 Coriolis forces in GLM theory
      5. 10.5 Lagrangian-mean gas dynamics and radiation stress
      6. 10.6 Notes on the literature
    7. 11 Zonally symmetric GLM theory
      1. 11.1 GLM theory for the Boussinesq equations
      2. 11.2 Rotating Boussinesq equations on an f-plane
      3. 11.3 Langmuir circulations and Craik–Leibovich instability
      4. 11.4 Notes on the literature
  11. PART THREE WAVES AND VORTICES
    1. 12 A framework for local interactions
      1. 12.1 A geometric singular perturbation
      2. 12.2 Examples of mean pressure effects
      3. 12.3 Vortical mean-flow response
      4. 12.4 Impulse and pseudomomentum conservation
      5. 12.5 Notes on the literature
    2. 13 Wave-driven vortex dynamics on beaches
      1. 13.1 Wave-driven longshore currents
      2. 13.2 Classic theory based on simple geometry
      3. 13.3 Theory for inhomogeneous wavetrains
      4. 13.4 Vorticity generation by wave breaking and shock formation
      5. 13.5 Vortex dynamics on sloping beaches
      6. 13.6 Barred beaches and current dislocation
      7. 13.7 Notes on the literature
    3. 14 Wave refraction by vortices
      1. 14.1 Anatomy of wave refraction
      2. 14.2 Remote recoil
      3. 14.3 Wave capture of internal gravity waves
      4. 14.4 Wave–vortex duality and dissipation
      5. 14.5 Notes on the literature
  12. References
  13. Index