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Quasi-linear Theory for Surface Wave-Current Interactions

  • Book
  • © 2022

Overview

Authors:
  1. James C. McWilliams

    1. Atmospheric and Oceanic Sciences, University of California, Los Angeles, Los Angeles, USA

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  • Introduces a new theory that extends previous ones setting the standard for simulations of the Langmuir turbulence
  • Provides wave-averaged expressions for the wave amplitudes and for the dynamical evolution of the currents
  • Illustrates the formal theory with examples and envisions its implementation in realistic wave and circulation models

Part of the book series: Mathematics of Planet Earth (MPE)

Part of the book sub series: SpringerBriefs in Mathematics of Planet Earth (SBMPE-WCO)

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-x
    Download chapter PDF

  2. Introduction

    • James C. McWilliams
    Pages 1-5

  3. General Balances

    • James C. McWilliams
    Pages 7-8

  4. Quasi-Linear Wave and Current Balances

    • James C. McWilliams
    Pages 9-15

  5. Scaling Analysis

    • James C. McWilliams
    Pages 17-20

  6. Quasi-Linear Wave Theory: CEW

    • James C. McWilliams
    Pages 21-26

  7. Quasi-Linear Current Theory: WEC

    • James C. McWilliams
    Pages 27-38

  8. Wave–Current Resonance

    • James C. McWilliams
    Pages 39-41

  9. Examples

    • James C. McWilliams
    Pages 43-45

  10. A Program for Broad-Band Wave and Current Spectra

    • James C. McWilliams
    Pages 47-48

  11. Material Concentration and Buoyancy

    • James C. McWilliams
    Pages 49-52

  12. Summary and Prospects

    • James C. McWilliams
    Pages 53-55

  13. Back Matter

    Pages 57-126
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Keywords

About this book

This book introduces a mathematical theory for the interaction of oceanic surface gravity waves and oceanic currents. This theory is formulated using the quasi-linear approximation for a uniform density fluid with a free surface and it provides wave-averaged expressions for the wave amplitudes and for the dynamical evolution of the currents. The surface gravity wave–current interaction theory is a more complete theory than previous with respect to an asymptotic expansion in the small parameter V/C, where V is a current speed and C is a wave speed. This book also illustrates the formal theory with several examples, and the path for its implementation in more realistic wave and circulation models is envisioned.

This book is appealing to oceanic research scientists and mathematicians interested in geophysical fluid dynamics.

Authors and Affiliations

  • Atmospheric and Oceanic Sciences, University of California, Los Angeles, Los Angeles, USA

    James C. McWilliams

About the author

James C. McWilliams is the Louis Slichter Professor of Earth Science in the Department of Atmospheric and Oceanic Sciences and Institute of Geophysics and Planetary Physics at the University of California at Los Angeles. He has written widely on geophysical fluid dynamics theory and computational simulations of turbulent flows. He is a Fellow of the American Geophysical Union and Member of the U.S. National Academy of Sciences.

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