Integral equation model for wave propagation with bottom frictions

An integral equation method is developed to calculate wave propagation and runup in a two-dimensional wave channel. First, the problem is formulated as a potential flow with nonlinear free-surface boundary conditions. The effects of bottom friction are included in the model via a boundary-layer approximation. Numerical solutions are obtained for the maximum runup heights of solitary waves and enoidal waves on a constant slope. Numerical solutions are compared with available experimental data. A very good agreement is observed. The maximum runup height of a enoidal wave is larger than that of an equivalent sinusoidal wave. However, the runup height of enoidal wave is smaller than that of solitary wave with the same wave height. The runup height of enoidal waves is not a monotonic function of the incident wavelength. Numerical solutions for the maximum runup heights confirm that the bottom frictional effects are important when the slope is less than 20°.