All the values are positioned between lines y = 1.1 x and y = 1.2 x, which corresponds approximately to the above empirical interrelations. Figure 5-right illustrates the relations of the same statistical parameters behind the breakwater. There is a change in these relations when in higher periods the relationship tends to Tmax ≈ T1/10 ≈ Ts ≈ 1.5 Tm. This happens because when the waves cross the breakwater, a more significant reduction in the mean period Tm occurs (Figure 4) in relation to the other periods Tmax, T1/10 and Ts. Tm is more significantly reduced by the appearance

of high frequency harmonics (short waves), which are not so important from the engineering point of view because of their small height. So one should be careful when applying selleck chemical the mean period Tm to engineering purposes in the case Pirfenidone of submerged structures. As a consequence of wave spectrum deformation, i.e. wave nonlinearity effects in shallow water, an error could occur when estimating the mean spectral period, T0.2 (see list of symbols), which may be underestimated by as much as 70% of the statistical mean period Tm (Longuet-Higgins 1983). Since wave spectra are deformed when waves cross a breakwater, the question arises whether a similar mistake might be expected in the estimation of the transmitted mean spectral period T0.2 − t. Figure 6 illustrates the ratio of mean statistical and spectral wave periods for incident

and transmitted waves: mean spectral T0.2 − i fantofarone is compared with Tm − i for incident waves, and T0.2 − t is compared with

Tm − t for transmitted waves. It can be concluded that wave spectra deformation does not influence the calculation accuracy of spectral mean periods T0.2 − t. It has already been mentioned that in the process of wave transmission over a breakwater, the wave energy is transmitted to higher frequencies, along with the increase in the term m2 (second moment), resulting in a reduction in the mean spectral wave period of transmitted waves T0.2=m0/m2 and the reduction of the T0.2 − t/T0.2 − i ratios in the function of relative submersion Rc/L0.2 − i (Figure 7). The data from Van der Meer et al. (2000) for smooth emerged breakwaters with a similar breakwater geometry and similar wave parameters as in this paper are used for comparison. In such a way, the reduction of the mean spectral wave periods T0.2 for a wider range of relative submersion Rc/L0.2 − i, namely from − 0.15 to − 0.06, is obtained. It can be seen in the above figure that the ratio T0.2 − t/T0.2 − i tends to a value of ~ 0.68 when the relative submersion Rc/L0.2 − i tends to zero, taken from either the positive or the negative side. The results of Van der Meer’s measurements for the emerged breakwater are closer to this value, since the measurements were made for the lower parameter Rc/L0.2 − i. The obvious dependence of parameter T0.2 − t/T0.