An extended two-layer viscous Boussinesq-type model for surface gravity waves: Including the effect of bottom friction

Wave propagation is accompanied by energy attenuation owing to the water viscosity. Based on the two-layer viscous Boussinesq-type model considering of deep-water waves, the bottom friction term is incorporated to further simulate wave energy dissipation for limited-depth and shallow water waves. The viscous effects at the free surface and the seabed are analyzed based on analytical linear dispersion. Linear dispersion relation of present model is obtained using Stokes-type Fourier analysis and compared with the analytical solution, where the linear phase celerity and damping rate of the model is accurate for h/L₀ ≤ 8.0 and 5.22 (h is water depth and L₀ is characteristic wavelength) within 1% error, respectively. The finite difference method is employed for numerical implementation, and the computed results are compared with analytical solutions and related experimental data. Remarkable agreements demonstrate the accuracy of the numerical procedure and verify the importance of bottom friction. This article discusses the dimensionless water depth corresponding to the maximum damping rate caused by bottom friction and comparing the different methods to consider bottom friction. The value of bottom friction coefficient is also explored based on experiments.