The linear wave theory and the nonlinear-unsteady porous flow model are applied to analyze the energy dissipation and the bed pore water pressure induced by the interaction of wave, uniform current and porous bottom without considering the nonlinear waves and the viscosity effect inside the boundary layer. In this model, the linear, inertial and turbulent resistances are combined into a linearized resistance coefficient and the present system can be analyzed by a linear boundary value problem. The numerical result is quite agreement with the existing experimental data. It shows that the energy dissipation is reduced by the Doppler shift and the distribution of energy loss moves to the lower relative water depth region in the wave-following current. On the other hand, the bed pore water pressure in the wave-following current is always lager than that in the pure wave and the wave-opposing current.Keywords:wave-current interaction, rigid porous medium, nonlinear-unsteady porous flow model, energy dissipation
1.IntroductionThe Doppler shift is the relative motion which is the change in the frequency of waves for an observer moving relative to the source. In the water wave, it represents the wave-current interaction. Non-uniform or uniform currents influence the characteristics of waves. The speed and wavelength are increased in waves encountering a favorable current and vice verse for the opposing current (Nielsen, 2012).A lot of theoretical and experimental studies for wave-varying current interaction in the infinite and finite water depth with the smooth impermeable seabed had been performed. Typical samples are found in Stewart(1960,1961), Jonsson et al.(1970Jonsson et al.( ,1978, Jonsson(1977), Peregrine(1976), Thomas(1981Thomas( ,1990, Baddourand Song (1990), Groeneweg and Battjes (2003) (2013, 2014) used the perturbation approach to analyze the high-order nonlinear wave-current interaction in 3D Lagrangian scheme, and the mass transport velocity and the particle orbit both were measured in the 1D wave-current tank. In the laboratory experiment (Huang et al.,1972), it displayed the relative importance of wave-current interaction is decided by the nondimensional parameter 0 / U C with U as the current velocity and 0 C the wave speed without the current. The kinematics of the strong interaction in the wave-current motion were measured by Lai et al.(1989). Their results confirmed the critical 0 / U C with the currents induced the blockage of waves is -0.25. Soares and Pablo (2006) carried out an experimental study for the wave-current motion, and determined the change of wave spectra due to the coexistence of wave-current in the 3D wave basin. The experimental results showed that the energy absorbed by waves in the opposing current is impossible to continue the growth, and it is up to a certain limit, eventually resulting in wave breaking. However, the porous seabed and the energy dissipation are not considered in there existing studies.The experiment for the wave-current interaction over a rough bed was perfo...