Spectra

The freak waves generally occur when the maximum wave height $H_{max}$ exceeded 10m during the winter storm conditions where the mean wind speeds exceeded 13m/s, as those listed in Table 2. 5 presents the corresponding frequency spectra for the cases of Y871124, Y880109, Y880202 and Y881214. All of these spectra show the familiar spectrum form of wind waves with a well-established equilibrium range on the high frequency side of spectrum. The equilirium range clearly follows the typical wind wave frequency power law that is proportional to $f^{-4}$.

Figure 6: Directional spectrum of Y871124.

Further, in order to investigate directional distributions of the spectral characteristics, directional spectra $S(f,\theta)$ were computed using the Extended Maximum Entropy Method (Hashimoto, 1992). 6 presents an example of the directional spectrum obtained from a 30 min data recording that include a freak wave for the case of Y871124. It is shown that the sea waves including a freak wave incidence have the same single peak directional spectrum of wind waves and their directions concentrate around the mean wave directions $\theta_{m}$ from 270 deg. (W) to 300 deg. (WNW) in this case. All of the observed data including the freak waves have the similar single peak spectrum and their directions concentrate around the mean wave directions without exception.

Therefore, it can be inferred that the freak waves can occur in the sea conditions with usual single peak spectra without multi-directional effects.

Table 2: Wave and wind statistics at the occurrence times of giant freak waves.

Data code	Period(hrs)	N	$\overline{U}$(m/s)	$\overline{\theta}$(deg)	$H_{1/3}$(m)	$H_{max}$(m)
Y871124	23.5	10613	12.99	296.3	5.06	11.30
Y871217	22.0	9770	19.28	295.3	7.35	14.73
Y880109	37.5	18535	13.38	292.4	4.44	10.41
Y880202	24.5	10184	16.62	292.8	6.40	14.22
Y881214	30.0	15615	15.63	226.5	5.28	11.16
Data code	$H_{max}/H_{1/3}$	$T_{1/3}$(s)	$(ka)_{1/3}$	$\mu_3$	GF
Y871124	2.23	10.25	0.106	0.292	0.901
Y871217	2.00	11.24	0.133	0.306	0.762
Y880109	2.34	9.09	0.115	0.245	0.865
Y880202	2.22	10.49	0.129	0.381	0.745
Y881214	2.11	10.60	0.105	0.262	0.727