The influences of Doppler shift on the wave dissipation and soil responses over the porous medium

The influences combined the porous seabed and the uniform current on the energy dissipation and the soil responses in the wave-current interaction over the ideal porous seabed are presented in this paper by using the 1D linear wave theory and the linearized porous flow. The relative wave damping rate can be numerically determined by using the complex dispersion relationship. The influences of Doppler shift and the thickness of porous seabed on the wave damping rate, the pore water pressure and its phase shift are discussed, respectively. In addition, the differences using numerous common porous flow model is also compared. Present results find that the energy dissipation is affected by the Doppler shift because the soil responses and the discharge velocity is changed due to the current induced the adjustment of wavenumber or the wavelength. In the case of following current, the interfacial vertical velocity is decreased with the increase of the current velocity. On the other hand, before reaching up the kinematic limit, the magnitude of interfacial vertical velocity is proportional to the flow velocity in the cases of opposing current. Respectively, clarifying the relative importance of the Doppler shift and the thickness of porous media on the energy loss and the soil responses are found that the influence of the thickness of the porous seabed on the energy dissipation has better efficiency. Relative to the thickness of the permeable seabed, the flow velocities and its direction is the important factor on calculating the soil responses.