Separation of free and bound harmonics in waves

Free and bound (phase-locked) waves with the same frequency cannot be distinguished simply in a frequency domain. A 1-Hz wave propagating over a submerged rectangular step was physically investigated and used to generate higher free and bound harmonic components in waves. The time history of a 3.28 m surface profile above the submerged step was measured and analyzed using two-dimensional Fourier Transform and Morlet wavelet transform sequentially. Incident and reflected waves as well as the associated free and bound components of each harmonic (through the 3th harmonic) were separated successfully. The spatial phase information of the 2nd free-mode and bound-mode harmonics were obtained which gave a good physical explanation of amplitude recurrence. It was observed that wave lengths of harmonics vary in space and phase shift occurs as the 1st harmonic catches up the 2nd free-mode harmonic. It was also found that the 2nd free-mode harmonic gained more energy from the 1st harmonic before entering deep water.