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/s10 955-021-02699-0.], 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 thealgebra 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 dispersionrelationfor 1D surface gravity waves propagating on an irregular floor. The theory is based on the study of the mean-value of planewave-like Fourier modes for the propagation and damping of surfacewaves on a random bottom.