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 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. [ABSTRACT FROM AUTHOR]