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

Abstract

In the present study, the effect of waving bottom on the surface wave is studied. Basing on the fundamental equations of potential flow theory and boundary conditions, using the multiple scales perturbation method to derive the first-order and the second-order approximate equation which the fluid surface waves satisfied in the presence of waving bottom. Under the second-order approximation, the fluid surface waveform in first-order approximate equation is numerically simulated with MATLAB in the presence of different waving bottom form. The results show that: the fluid surface waveform is composed of a harmonic wave which has the same frequency with waving bottom and a pair of KdV solitary waves that spread to both the right and the left side when the waving bottom wave is a harmonic wave; and when the waving bottom is a solitary wave packet, it consists of a solitary wave which is closely related to the specific form of waving bottom and a couple of KdV solitary waves. With the development of time, three waves in fluid surface do not affect each other and they propagate independently. Thus it can be seen the waving bottom is effective for maintaining surface wave energy balance income and expenditure in the spreading process.