An Experimental Investigation of Nonlinear Wave Generation by Flap Wavemakers

It is well known that flap wavemakers behave in a nonlinear way when either the flap angle or the flap velocity becomes large. Moreover, the hinge depth should be adapted to the period of the generated waves in order to minimize linear evanescent modes, which may contribute to the formation of nonlinear spurious waves. For example, imposing a sinusoidal motion with a relatively long period and a large amplitude to a short flap will result in a surface elevation composed of a regular wave with the same period as the flap motion, but also of a variety of harmonics with higher frequencies. Second-order harmonics can be predicted theoretically for regular and irregular waves, and they can be corrected by modifying the control signal of the wavemaker. However, there is no theory that can describe nor mitigate effects of orders higher than two. The design of the wavemaker is then essential to generate extreme sea states with good quality and predictability in a laboratory.

In this paper, the nonlinearities of flap wavemakers are investigated experimentally for regular and irregular waves generated in SINTEF Ocean’s laboratories. Nonlinearities of order two and three are estimated from times series of the surface elevation measured at different locations by an array of wave probes. Particular focus is put on identifying the effects of the classical second-order correction on the second- and third-order harmonics.