Gravity waves on a random bottom: exact dispersion-relation

Abstract

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.

Keywords:

• Gravity waves
• random bottom
• strong localization
• weak localization
• dispersion-relation

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

M.O.C. thanks to funding provided by CONICET (Grant No. PIP 112-201501-00216, CO),  and Grant: Secretaría de Ciencia Técnica y Postgrado: 06/C565. U. N. Cuyo (2019).