Nonlinear waves propagating over a deformable seafloor

Interaction of nonlinear shallow water waves with a deformable seafloor represented by an infinitely long elastic sheet lying on a viscoelastic foundation is investigated. The study is motivated by damping features of muddy coastal areas on ocean waves. The mathematical model utilizes the Level I Green–Naghdi equations for the fluid flow and the thin plate theory for the elastic bottom deformations. The methodology is validated through comparisons with the linear water wave theory and available numerical data. Theoretical predictions of the coupled seafloor vertical displacement and free-surface elevation are provided for a range of the incoming wave parameters and the seafloor characteristics. The results demonstrate that the wave experiences significant decrease in amplitude and propagation speed, as a result of the interaction with the deformable seabed. An exponential decay of periodic waves with propagating distance is observed. It is found that the foundation stiffness is of dominating importance, as compared to other parameters of the deformable seafloor. It is shown that waves with shorter wavelength are dissipated strongly by the action of the deformable seafloor while the bottom conditions have less impact on long wave dissipation. Just the opposite, long waves experience significant wave diffraction when compared to the waves with shorter wavelength. Patterns of the velocity field are shown to be modulated in magnitude and wavelength contributed by the seafloor.