Generation of highly nonlinear irregular waves in a wave flume experiment: Spurious harmonics and their effect on the wave spectrum

Spurious harmonics generation can occur in wave basins when strongly nonlinear waves are generated with linear wave maker theory. For regular long crested waves, the phenomena is known to cause a beating pattern for the amplitude of the higher harmonics, while for irregular waves the effect is often thought to average out.

We here report on recent experimental results for spurious harmonic generation for highly nonlinear irregular waves. Long crested waves at two depths are considered. We find a systematic distortion of the spectral shape which is non-uniform in space. The effect occurs in the linear and super harmonic region of the spectrum and is strongest at the smaller depth.

We analyze the phenomenon through re-computations in a fully nonlinear wave model and the further application of a four-phase harmonic separation. We next extend the analysis to allow separation of the third- and first-order content of the first-harmonic wave field, by computation at two different amplitudes.

The numerical results resembles the measured spectrum closely and the harmonic separation shows that the spectral distortion in the super-harmonic region is to large extent a property of the second-harmonic wave field. Further, the match between the first-harmonic spectrum and the original target spectrum is shown to improve strongly by the removal of the extracted third-order contribution.

The observed spectral distortion in the linear frequency region can thus be explained by this third-order field. Returning to the second-order wave field, we demonstrate that the extracted second-order wave field with associated spectral distortion can be reproduced by application of the Sharma and Dean theory with inclusion of the reconstructed spurious wave field from the linear wave generation.

Finally, the effect of the spurious second-order harmonic generation on the measured forces is discussed and quantified. We find that the force peak exceedance probability is less influenced by the spurious waves than the spectral shape. We link this to the smaller phase speed of the spurious waves, that makes them arrive later than the main wave packet and thus leads to a limited enhancement of the local peaks.