## 3 Discussion of Results
It can clearly be seen that, as the waves propagate, the periodic exchange of energy between the main and second non-linear harmonics takes place. As the waves approach the shore, the amplitude of the second harmonic begins to increase, and the first begins to decrease, then the energy begins to transfer back from the second harmonic to the first one. On 28 September, the absolute maximum of the second harmonic amplitude was spotted within the coastal zone (distance 150 m from the coast, Figures 4a and 5a), and one pronounced energy exchange period was observed between them. On 29 September, the absolute maximum of the second non-linear harmonic was spotted closer to the coast and almost two complete periods of energy exchange between the harmonics were observed. Figure 4: The evolution of wave spectra: (**a**) 28 September 2007, wave run 34; (**b**) 28 September 2007, wave run 42. The change in the biphase for these cases, calculated with the use of Formula (6), is shown in Figures 5b and 6b. As waves propagate towards the shore, the biphase varies between [-\(\pi\)/2, +\(\pi\)/2], which, according to Formulas (3) and (4), will always result in a positive sediment discharge, directed toward the shore. As shown in [24; 37], such a change in the biphase is characteristic of non-linear wave transformation over an inclined bottom and wave breaking by spilling and plunging types, which is confirmed by laboratory and field data. During the periodic energy exchange between non-linear harmonics, when the second harmonic arises and starts to grow, at the beginning the biphase is negative (Figure 5b distance 150-175 m, Figure 6b distance 140-175 m from the coast) and then it gradually increases to zero. Figure 5: The evolution of normalized amplitudes of first and second non-linear harmonics (**a**), biphase (**b**); the third and fourth moments of the orbital near-bottom velocity (**c**), calculated with the use of Formulas (3) and (4) for the wave situation on 28 September (series 34–39). Calculated deformations of the bottom relief and moving averaged difference in measured profiles between 28 and 29 September (**d**). The bold line shows the averaged values (series 34–39) that the calculations of velocity moments and deformations are based on. The zero value of the biphase corresponds to the maximum amplitude of the second harmonic (distance 140 m, Figure 5a,b and 150 m, Figure 6a,b). After that, the amplitude of the second harmonic begins to decrease, and the backward stage of the periodic exchange takes place, followed by an increase in the amplitude of the first harmonic. In this case, the biphase increases and its values are the interval of 0.6-1.4 radian (Figure 5b, distance 110 m) and 0.8 radian (Figure 6b distance 125 m). In general, as shown in [24] the value of the biphase at the point where the second harmonic reaches its maximum amplitude is close to \(\pi\)/2. In the selected examples, we do not observe this critical value in the biphase, possibly because we do not have detailed information, due to the limited spatial resolution of our wave measurements. Figures 5c,d and 6c,d show changes in the sediment discharge components calculated with the use of Formulas (3) and (4) and estimated bottom deformations based on changes in the gradient of the sum of these two components. We do this only at a qualitative level, because of heterogeneous sediments on the sea bottom. However, as can be seen from Formula (2), the coefficient before the first term (the bedload sediment transport) is equal to 0.2. The coefficient before the second term (the transport of suspended sediments) depends on the sediment fall velocity. For the considered study  
Figure 6: The evolution of normalized amplitudes of first and second non-linear harmonics (**a**), biphase (**b**); the third and fourth moments of the orbital near-bottom velocity (**c**) calculated with the use of Formulas (3) and (4) for the wave situation (series 42) on 29 September.