On the generation of long waves

For relatively long waves generated by a piston-type wave maker, the classical linear wave-maker theory is extended to second order accuracy. Within the limits of validity of the theory, this agrees well with experimental results for the motion generated by a sinusoidally moving wave maker, and shows that secondary waves are associated with the existence of a second harmonic free wave. By giving the wave maker a motion that consists of a first and a second harmonic, it is shown that this free second harmonic wave may be eliminated, so that the generated wave is virtually of permanent form.