Experimental investigation of nonlinear regular wave transformation over a submerged step: Harmonic generation and wave height modulation

In this study, a series of flume experiments were conducted to investigate the harmonic generation and wave height modulation (i.e., recursion) of nonlinear waves passing over a submerged step. A total of 35 experimental conditions were considered, including several different incident amplitudes/periods and bottom configurations, i.e., four step widths and three step heights (or three submergence depths). The waveforms across a 7.8-m-long segment were recorded over a period of 21.8 s using the non-intrusive imaging system. The measured surface elevations were further analyzed to reveal the amplitude variations of harmonic frequencies based on the 2D Fast Fourier and 1D Morlet wavelet transforms. A set of parameters was proposed to depict the generation of second-harmonic waves at the step crest. Overall, it was found that the most influencing factors for harmonic generation are the Ursell number of incident waves and relative height of the obstacle while the relative step width yields an insignificant impact. The wave height modulation (i.e., recursion) of second harmonic is affected mainly by the wavelengths of its free and bound components, which are accurately estimated from the Morlet wavelet transform analysis and third-order Stokes dispersion relation. The amplitude of primary wave exhibits a different recursion pattern due to the generation of the third, forth, and higher harmonics. Based on the concept of average energy flux, the recursion phenomenon of harmonics is further clarified.