Waves Propagate over a Submerged Step：The Effect of the Geometry of Step on Harmonic Generation

A series of flume experiments were conducted to investigate the harmonic generation, wave height modulation (i.e., recursion) and the variation of energy flux of nonlinear waves passing over a submerged step. A total of 45 experimental conditions were considered, including several different incident amplitudes, periods (0.8, 1.0 and 1.25 Hz) and bottom configurations, i.e., four step widths and three step heights (or submergence depths). The waveforms across a 7.8-m-long segment were recorded over a period of 21.8 sec using a 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 and forth harmonics. In the end, the concept of average energy flux is clarified the recursion phenomenon and take the result to parameter optimization. In the point of energy flux, we discussed the effects of reflection (Kr), transmission (Kt) and energy dissipation (Kd) at the lee side and weather side when waves propagate over a submerged.