Theoretical Analysis of Average Wave Steepness Related to Peak Period or to Mean Period

The average wave steepness may be defined as the ratio between the significant wave height H_s and the wavelength associated to either the zero-up-crossing mean period L_m or the peak period L_p (Bitner Gregersen et al., 1998). This parameter may be calculated from wave data at fixed locations, as well as by starting from theoretical spectra. In this paper the average wave steepness is firstly analyzed by considering a JONSWAP spectrum. It is shown that for this spectrum the ratio S_m = H_s/L_m, as well as S_p = H_s/L_p, depends upon the values of the spectrum parameters. The theoretical values are then compared with wave data in the Mediterranean Sea, Pacific Ocean, Atlantic Ocean and North Sea. The values of S_m and S_p are deeply investigated for severe sea states, with large values of H_s. It is obtained that in severe sea state the observed values of wave steepness, defined as either S_m or S_p, are always in the range defined by theoretical spectra; therefore, the extreme values of S_m and S_p, which are of interest for naval architecture, may be obtained from theoretical analysis, as a function of extreme values of H_s.