## 1 Introduction  
Waves play an important role in coastal zone morphodynamic; in particular, they influence on erosive and accumulative processes of the sand deposits. Recent investigations demonstrated the main role of wave transformation processes--for example, wave propagation in the form of bore and low-frequency motions correlated with the transformation of irregular waves with a group structure that can affect sediment transport in the nearshore and swash zones [1; 2; 3; 4]. It was shown that, due to non-linear wave transformation, the sediments can move in the cross-shore direction and affect the underwater bottom profile shape. This is due to the asymmetry of near-bed orbital velocities, which is connected with wave asymmetry (for example, [5; 6; 7]). However, the relation between cross-shore sediment transport and the wave nonlinearity is not fully understood up to now because the interaction processes between waves, sandy particles and the seab are complex. However, there are many commonly used formulae to predict sediment transport resulting from near-bed orbital velocity asymmetry under non-linear Stokes-type waves [8; 9; 10; 11; 12; 13; 14]. There are also many models based on the parametrizations of wave asymmetry changes. The most successful parameterization is based on the Ursell number and parameter analogues, a biphase (phase shift between the first and second non-linear harmonics of waves) suggested in [15]. However, the verification of this parametrization on various experimental data does not always give a good match [16; 17]. The main reason for this may be the non-linear wave transformation due to near-resonance interactions. Most parts of the coastal zone can be attributed to the so-called intermediate water depth, the approximate boundaries of which are 0.05 \(<\) h/L \(<\) 0.5, where h is the depth and L is the wavelength. While propagating at these depths, waves transform under the influence of weakly non-linear dispersive processes associated with the growth of multiple non-linear harmonics due to near-resonant triad interactions (for example, [18; 19])  
\[\pm k_{1}\pm k_{2}\mp k_{3}=\delta,\ \pm\omega_{1}\pm\omega_{2}\mp\omega_{3}=0 \tag{1}\]  
where \(k=k(\omega)\) is determined by the dispersion relation (\(k\) is the wave number and \(\omega\) is the angular frequency), \(\delta\) is the detuning or deviation from the full resonance conditions caused by the dispersion effects. Near-resonance interactions in waves at an intermediate depth generate a periodic energy exchange between the main (first) and second non-linear harmonics. This process is accompanied by the periodic oscillations of their amplitudes as the waves propagate to a shore. It has been theoretically shown that the characteristic spatial length of these oscillations is proportional to the 2\(\pi\)/\(\delta\), i.e., with decreasing water depth at \(\delta\)\(\rightarrow\)0, such oscillations will not be observed [19; 20]. The existence of a periodic energy exchange between harmonics in irregular waves was confirmed by field experimental studies of the irregular wave transformation in the coastal zone [21; 22]. According to these experimental data, the characteristic scenarios of wave transformation with a periodic energy exchange between the first and second non-linear harmonics were identified and the conditions for their implementation, depending on the average slope of the sea bottom and the steepness of waves at the entrance to the coastal zone, were determined. They revealed typical scenarios of non-linear wave transformation differ in the number of observed spatial periods of exchange between the first and second non-linear harmonics and in the position of the absolute maximum of the second non-linear harmonic, which can be reached in the inner part of the coastal zone or only near the coastline. As a consequence of the periodic energy exchange between non-linear harmonics, the amplitude-frequency composition of individual irregular waves is subject to changes as well, as the waves approach the shore.