Model Equations Combining Full Linear Dispersion With Long Wave Nonlinearity, Part.3 - Nonlinear evolution of waves on the step-type reef -

摘要

The system of integro-differential equations, which combines long wave nonlinearity with full linear dispersion, is proposed to study weakly nonlinear evolution of shallow-water waves. The dispersion term in the system is described by the integral with the kernel of the Fourier transform of dimensionless wave speed. The wave equation developed for spectral-wave components is applied to nonlinear waves on the step-type reef in two dimensions. Comparisons to verify the model are made between present numerical results with the finite element method and experimental data. Numerical simulation shows that there occur longer period waves rather than incident waves, because of nonlinear interaction between wave components and bathymetry of the reef. As a result, the wave amplification factor at the shoreline of the reef becomes greater than that of the linear wave theory. At the same time the peak position moves as if longer period waves were incident upon the reef.