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Hilbert transform view of water-wave theory

Published online by Cambridge University Press:  07 May 2024

R. Krechetnikov Open the ORCID record for R. Krechetnikov [Opens in a new window]
R. Krechetnikov*
Affiliation:
Mechanical and Civil Engineering, California Institute of Technology, Pasadena, CA 91125, USA Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB T6G 2G1, Canada
*
†Email address for correspondence: krechet@ualberta.ca
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Abstract

A general rethinking of the mathematical foundations of water surface waves from the perspective of the Hilbert transform uncovers shortcomings of the standard multiple-scale approach as well as elucidates the interplay of non-local and dispersive effects. Application of the Hilbert transforms to planar and cylindrical settings allows us to deduce new weakly nonlinear models, including an alternative to Zakharov's equation and an envelope equation for cylindrical waves on deep water, as well as to highlight the crucial differences between these geometries.

JFM classification

Waves/Free-surface Flows: Waves/Free-surface Flows
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 986 , 10 May 2024 , R3
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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