Quasi-linear Theory for Surface Wave-Current Interactions

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 wavecurrent 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.

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

Auteur

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.

Résumé

"A seminal contribution to the field of oceanography and fluid dynamics, offering a comprehensive and mathematically rigorous framework for understanding the complex interactions between surface waves and ocean currents. McWilliams's monograph is poised to influence future research in this area, highlighting the importance of quasi-linear theories in simulating and understanding geophysical fluid phenomena." (Denys Dutykh (Le Bourget-du-Lac), zbMATH 1536.76001, 2024)

Contenu

1. Introduction.- 2. General Balances.- 3. Quasi-linear Wave and Current Balances.- 4. Scaling Analysis.- 5. Quasi-linear Wave Theory: CEW.- 6. Quasi-linear Current Theory: WEC.- 7. WaveCurrent Resonance.- 8. Examples.- 9. A Program for Broad-Band Wave and Current Spectra.- 10. Material Concentration and Buoyancy.- 11. Summary and Prospects.