摇板式造波机所造二维规则波波形的频域二阶解

Second-order Solution of the Elevation of Two-Dimensional Regular Wave Generated by Rocker Flap Wave Generator

本文给出摇板式造波机所造二维规则波波形在频域中的二阶摄动解.结果表明二阶波包括三部分,第一部分是定常波,第二部分是波数为一阶波数二倍的进行波,第三部分是二阶波数对应的进行波.前两部分与一阶波一起组成了二阶Stokes波,后一部分体现了摇板对流场的二阶响应,其传播速度比Stokes波慢.由于两部分二阶进行波的波速不同,在水池中距摇板不同距离处测得的波形是不同的.实际造波试验证实了上述结论.

Adopting the perturbation method the second-order solution in frequency domain of the elevation of two-dimensional regular wave generated by the rocker flap wave generator is derived.The results indicate that the second-order wave consist of three components: the first is a stationary wave, the second is an outgoing progressive wave propagating with the wave number, which is twice the first-order wave number and the third is an outgoing pro-gressive wave of second-order wave number.The first two parts form the second-order Slokes wave with the first-order outgoing progressive wave.The last part reflects the second-order effect of the flap on the flow field and travels slower than Stokes wave.Since the phase velocities of the two parts of second-order outgoing waves are not alike, the wave elevations measured by the gauges with distinct distances away from the flap will be different from each other.These conclusions are confirmed by experiments in the flume.