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This paper presents the analysis of measurements of long waves at the harbor of Marina di Carrara, Italy. Nine pressure gauges (eight in the inner harbor and one outside the harbor) were used to record continuously the water surface elevation, for about 3 years; incoming short waves were measured using a directional buoy at about 500 m offshore the breakwaters. The analysis is carried out splitting the energy of the long waves into two bands, i.e., very long waves (VLW; f < 0.003 Hz) and long waves (LW; 0.003 < f < 0.030 Hz); it is found that LW energy is strongly correlated with the energy of the incoming short waves while no correlation (or very poor) is found for VLW. During energetic sea states, surface elevation spectra of VLW and LW, normalized against the wave energy of each frequency band, appear to be autosimilar; this suggests that the spectra of the incoming long waves have a mostly constant shape. Simple numerical computations of harbor resonance, carried out using a mild-slope equation linearized model, indicate that the amplification of the height of the incoming LW generated by short waves (calculated using empirical formulae from previous researches by Melito et al. ) inside the harbor can be reasonably predicted using such simple approach, assuming that the LW spectra are rectangular. The shape of the amplification diagram calculated by the numerical model shows reasonable (but not perfect) agreement with the shape of the normalized measured spectra inside the harbor. [ABSTRACT FROM AUTHOR]

Abstract: The paper presents the comparison between the results of small-scale model tests and prototype measurements of wave overtopping at a rubble-mound breakwater. The specific structure investigated is the west breakwater of the yacht harbour of Rome at Ostia (Italy) and is characterized by a gentle seaward slope (1/4) and by a long, shallow foreshore. The laboratory tests firstly aimed at carefully reproducing two measured storms in which overtopping occurred and was measured. The tests have been carried out in two independent laboratories, in a wave flume and in a wave basin, hence using a two-dimensional (2-D) and a three-dimensional (3-D) setup. In the 2-D laboratory tests no overtopping occurred during the storm reproductions; in the 3-D case discharges five to ten times smaller than those observed in prototype have been measured. This indicates the existence of model and scale effects. These effects have been discussed on the basis of the results of several parametric tests, which have been carried out in both laboratories, in addition to the storm reproductions, varying wave and water level characteristics. Final comparison of all the performed tests with 86 prototype measurements still suggests the existence of scale and model effects that induce strong underestimation of overtopping discharge at small scale. The scale reproduction of wave breaking on the foreshore, together with the 3-D features of the prototype conditions and the absence of wind stress in the laboratory measurements, have been individuated as the main sources of scale and model effects. The paper also provides a comparison between the data and a largely used formula for wave overtopping discharges in the presence of structures similar to the one at hand. The suitable value of a roughness factor that appears in that formula is investigated and good agreement is found with other recent researches on rubble-mound breakwaters. [Copyright &y& Elsevier]