Localization of gravity waves on a random floor: weak and strong disorder analysis

Abstract

In the absence of any forcing and rotational effects, the 1D linearized Boussinesq’s equation for the evolution of a surface gravity wave propagating in a random bottom has been studied. The time-dependent evolution of plane-wave-like modes of gravity waves in the presence of weak disorder and for Fourier number outside the localized gap are shown to be well approximated by monochromatic telegrapher’s waves. For strong disorder the one-to-one correspondence for any Fourier number has been revisited.