Diffusion and localization of surface gravity waves over irregular bathymetry.
An interaction of a linear surface gravity wave with weakly irregular one-dimensional bathymetry has been analyzed using the diagrammatic technique. The Boltzmann diffusion coefficient and the Anderson localization length for the wave energy density are expressed analytically via a correlation function of irregularities of the sea floor. The results are applied to different topographies. The effect of a finite region of irregularities, viscous damping, wave interaction, current, geometrically diffuse wave source, and anisotropy on localization is briefly discussed. The theory provides a scenario for the observation of large scale Anderson localization phenomenon in a tank or possibly in coastal waters.
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