Measurement of long waves at the harbor of Marina di Carrara, Italy

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. 2007) 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.