Surface gravity waves on randomly irregular floor and the telegrapher's equation

Abstract

The simplest model for the evolution of the mean-value of a surface gravity wave propagating in a random bottom has been connected with the telegrapher's equation. This analysis is based on the comparison of the mean-value solution of dispersive plane-wave modes propagating in a binary exponential-correlated disordered floor with the solution of the homogeneous telegrapher's equation. Analytical results for the exact dispersion-relation are presented. In addition, the time-dependent analysis of mean-value monochromatic waves is also shown.