When free-surface waves are generated using wave paddles to produce the desired waves, higher order effects might be inevitable for some cases. These can be due to the mismatch in the wave paddle displacement and non-linear free-surface wave kinematics, as well as the moving boundary of wave paddles. Such higher order effects are often manifested as higher harmonic waves, which can propagate independently (or free waves). The presence of such waves will contaminate the quality of the tank test, and together with effects due to scaling and finite size of tank, it is important to reduce or mitigate such effects as much as possible in a wave tank in order to simulate a more realistic scenario.
This study investigates the above problem in a systematic manner by using a fully-nonlinear numerical wave tank based on the three-dimensional time-domain Harmonic Polynomial Cell (HPC) method. Wave is generated by flap-type wave paddles on one end of the tank, and is damped on the other end. The paddle boundary conditions are satisfied on the instantaneous paddles surfaces, and the free surface is tracked by the generalized semi-Lagrangian scheme. In this study, first order paddle signal is used to generate regular waves, and the focus is on characterising the behaviour of the generated free higher harmonic waves.
We first look into a rectangular wave tank where the paddles are distributed at one side of the tank. Upon the generation of an oblique regular wave (primary wave), it is observed that the generated free waves propagate at a different angle/direction. An explicit analytical expression is derived for the direction of the free waves, which agrees with the numerical observation. Besides propagating at a different direction, the free waves also interact with the primary waves resulting in additional bound waves of the first and third harmonics. Next, we consider a circular wave tank, where paddles along half of the circumference are used to generate planar regular wave, while paddles at the other half are assumed to be able to fully absorb the wave. The generated free waves are observed to focus at a particular region in the tank due to constructive interference.
To eliminate or at least mitigate such undesired waves, correction to first order paddle signal is required. Second order correction scheme based on Schaffer (1996) is implemented for such purpose. Preliminary results seem to suggest that second order correction to the paddle signal can only mitigate but cannot completely eliminate the existence of free higher harmonic waves.