Analytical study on wave making in a deep wave flume in step-type

Based on the eigenfunction expansion technique, an analytical study on wave generation by a piston wave maker in a deep wave flume in step-type is carried out. By matching 'wavemaker' solutions for the two regions at the cut above the step, the corresponding theoretical velocity potential and wave elevation in the flume are developed. The analytical solution is verified by a higher-order boundary element method (HOBEM). Numerical experiments are carried out to study the effects on the generated wave amplitude in deep water due to the step, the water depths at the up- and down-steps, the distance between the wave maker and the step cut, and the motion period of the wave maker. According to the proposed theory, the suitable water depths, and the wave maker position can be derived to reach the required wave height. Meanwhile, the relationship between the motion amplitude of the wave maker and the expected wave period & amplitude are also presented.