GAMMA SPECTRA:

Wave spectra of the gamma type are discussed in Section 2.8.1, Call [*281*#]. The Pierson-Moskowitz (PM), the Neumann and Lindemann spectra belong to this class. See Table 2.8.1.

Analytically the spectral density function of a gamma spectrum is equal to the general gamma probability density function, Section 2.6.2, Call [*262*#], normalised with the variance Mo of the vertical wave motion.

A gamma spectrum (PM) has been applied in the case in Section 1.3.8, Call [*138*#].

Gamma Spectrum Parameters:

  Pierson-Moskowitz type (l=5, n=4)
Significant wave height, Hs       (2.8.20)             12 m
Average zero-crossing period, Tz  (2.8.21)             10 s
 - Corresponding frequency, fz                        0.1 Hz
 - Angular frequency, omega_z                     0.62832 rad/s
 - Wave number, k                 (3.1.53)       0.040243 /m
 - Wave length, lambda                             156.13 m
 - Phase velocity, c_phi          (3.1.48)         15.613 m/s
 - Group velocity, c_g            (3.1.49)         7.8066 m/s
 
  Alternative parameters:
Scale parameter D                 (2.8.10)          1.786
 - Phillips parameter, alpha      (2.8.16)       0.018558
Spectral peak frequency, fm       (2.8.12)       0.071037 Hz
 - Corresponding period, Tm                        14.077 s
 - Angular frequency, OMEGA                       0.44634 rad/s
 - Wave number, k                 (3.1.53)       0.020308 /m
 - Wave length, lambda                              309.4 m
 - Phase velocity, c_phi          (3.1.48)         21.979 m/s
 - Group velocity, c_g            (3.1.49)         10.989 m/s
 
  Associated gamma distribution (2.8.1):
Shape parameter, a                 (2.8.7)              1
Slope parameter, h                 (2.8.6)             -4
Scale parameter, A                 (2.8.8)        0.47195
 - Alternative parameter, B        (2.8.8)        0.04961
Normalisation factor, Mo           (2.8.20)             9 m^2
 

Power Spectral Density Functions:

Angular frequency, omega                              0.5 rad/s
 - Dimensionless, omega/OMEGA = f/fm               1.1202
Angular frequency spectrum,S(omega)(2.8.15)         25.84 m^2s
Frequency, f                                     0.079577 Hz
Frequency spectrum,S(f)                            162.36 m^2s
Period, T                                          12.566
Period spectrum,S(T)               (3.7.11)        1.0281 m^2/s