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James C. McWilliams

Quasi-linear Theory for Surface Wave-Current Interactions

Quasi-linear Theory for Surface Wave-Current Interactions

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  • More about 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. 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.

Format: Paperback / softback
Length: 126 pages
Publication date: 06 October 2022
Publisher: Springer Verlag, Singapore


This comprehensive work presents a mathematical framework for studying the intricate interplay between oceanic surface gravity waves and oceanic currents. By employing the quasi-linear approximation for a uniform density fluid with a free surface, the theory offers wave-averaged expressions for both the wave amplitudes and the dynamic evolution of the currents. Notably, this theory surpasses previous formulations in its ability to describe an asymptotic expansion in the small parameter V/C, where V represents the speed of the currents and C denotes the speed of the waves. Furthermore, the book showcases the formal theory through numerous examples, providing a clear path for its implementation in more realistic wave and circulation models. This text is of immense interest to oceanic research scientists and mathematicians who are passionate about exploring the dynamic behaviors of the world's oceans.

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



Comprehensive in its scope, this work presents a mathematical framework for studying the intricate interplay between oceanic surface gravity waves and oceanic currents. By employing the quasi-linear approximation for a uniform density fluid with a free surface, the theory offers wave-averaged expressions for both the wave amplitudes and the dynamic evolution of the currents. Notably, this theory surpasses previous formulations in its ability to describe an asymptotic expansion in the small parameter V/C, where V represents the speed of the currents and C denotes the speed of the waves. Furthermore, the book showcases the formal theory through numerous examples, providing a clear path for its implementation in more realistic wave and circulation models. This text is of immense interest to oceanic research scientists and mathematicians who are passionate about exploring the dynamic behaviors of the world's oceans.

Weight: 221g
Dimension: 235 x 155 (mm)
ISBN-13: 9789811928758
Edition number: 1st ed. 2022

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