Gravity waves on a random bottom: exact dispersion-relation

In a recent paper [Cáceres MO, Comments on wave-like propagation with binary disorder. J. Stat. Phys. 2021;182(36):doi.org/10.1007/s10955-021-02699-0.], the evolution of a wave-like front perturbed by space-correlated disorder was studied. In addition, the generic solution of the field mean-value wa...

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Bibliographic Details
Published in:Waves in random and complex media 2024-03, Vol.34 (2), p.734-747
Main Author: Cáceres, Manuel O.
Format: Article
Language:English
Subjects:
Damping
dispersion-relation
Gravity waves
Infinite series
Operators (mathematics)
Plane waves
Propagation modes
random bottom
Series expansion
strong localization
Surface waves
Wave propagation
weak localization
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Summary:In a recent paper [Cáceres MO, Comments on wave-like propagation with binary disorder. J. Stat. Phys. 2021;182(36):doi.org/10.1007/s10955-021-02699-0.], the evolution of a wave-like front perturbed by space-correlated disorder was studied. In addition, the generic solution of the field mean-value was presented as a series expansion in Terwiel's cumulants operators. This infinite series cuts due to the algebra of naked Terwiel's cumulants when these cumulants are associated to a space exponential-correlated symmetric binary disorder. We apply an equivalent approach to study the dispersion-relation for 1D surface gravity waves propagating on an irregular floor. The theory is based on the study of the mean-value of plane-wave-like Fourier modes for the propagation and damping of surface waves on a random bottom.
ISSN:1745-5030
1745-5049
DOI:10.1080/17455030.2021.1918795