Numerical Study of the Influence of Waving Bottom on the Fluid Surface Wave

The effect of waving bottom on the fluid surface wave was investigated. Starting from the basic equations of potential flow theory and boundary conditions, we used the multiple scales perturbation method to deduce fluid surface waves satisfy the first-order approximate equation and second-order approximate equation. Under the second-order approximation, the fluid surface waveform was simulated with the Matlab in the presence of different waving bottom form. The results show that there are three solitary waves on the surface of the fluid. With the development of time, the amplitude of each solitary wave has not changed. It seems that they are not affected each other and propagate independently. So it suggests that the waving bottom is effective for maintaining surface wave energy balance income and expenditure in spreading process.