Quasi-linear Theory for Surface Wave-Current Interactions

By: James C. McWilliams

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Paperback | 6 October 2022

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Paperback
138 Pages

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23.39 x 15.6 x 0.76

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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.

Industry Reviews

"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)

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