Experimental study of freak waves due to three-dimensional island terrain in random wave
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Abstract: An experimental study is carried out for waves passing an isolated reef terrain in a wave tank. A three-dimensional model of a representative and isolated reef terrain in the West Pacific is built. Random wave trains with various periods and wave heights are generated by a wave maker using the improved JONSWAP spectrum. It is observed that there are different kinds of generation processes and waveforms of freak waves. The freak wave factor
${H_{\rm{m}}}/{H_{\rm{s}}}$ (where${H_{\rm{m}}}$ is the maximum wave height of wave series, and${H_{\rm{s}}}$ is significant wave height) is analyzed in detail, in terms of the skewness, kurtosis and water depth, as well as the relationship between freak wave height${H_{{\rm{fr}}}}$ and skewness. The freak wave factor${H_{\rm{m}}}/{H_{\rm{s}}}$ is found to be in positive correlation with the kurtosis, while larger${H_{{\rm{fr}}}}$ tends to be related with bigger skewness. The rapid variation of water depth, such as slope and seamount, contributes to the occurrence probability of freak waves.-
Key words:
- freak waves /
- random wave /
- skewness and kurtosis /
- three-dimensional island terrain
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Figure 5. The wave surface elevation of freak waves. a.
$H_{\rm s} = 3.59\,{\rm cm}$ ,$T_{\rm s} = 0.80\,{\rm s}$ ,$\theta = {0^\circ }$ ; and b.$H_{\rm s} = 6.35\,{\rm cm}$ ,$T_{\rm s} = 1.14\,{\rm s}$ ,$\theta = {0^\circ }$ .
Figure 7. The relationships between freak factor
${H_{\rm{m}}}/{H_{\rm{s}}}$ and skewness (a), and Hfr and skewness (b).
Figure 8. The relationship between freak factor
${H_{\rm{m}}}/{H_{\rm{s}}}$ , skewness and kurtosis. a. Freak factor${H_{\rm{m}}}/{H_{\rm{s}}}$ and kurtosis, and b. skewness and kurtosis. The red solid (
) represents cases with freak waves, the black solid (
) cases without freak waves.
Figure 9. The variation of significant wave height along the terrain (solid curve). a.
${H_{\rm{s}}} = 6.35$ cm,${T_{\rm{s}}} = 0.87$ s,$\theta = {22.5^\circ }$ ; b.${H_{\rm{s}}} = 6.35$ cm,${T_{\rm{s}}} = 0.87$ s,$\theta = {0^\circ }$ ; c.${H_{\rm{s}}} = 3.59$ cm,${T_{\rm{s}}} = 0.8$ s,$\theta = {0^\circ }$ ; and d.${H_{\rm{s}}} = 3.59$ cm,${T_{\rm{s}}} = 0.8$ s,$\theta = - {22.5^\circ }$ .
Figure 10. The variation of kurtosis along the terrain (solid curve). a.
${H_{\rm{s}}} = 6.35$ cm,${T_{\rm{s}}} = 0.87$ s,$\theta = {22.5^\circ }$ ; b.${H_{\rm{s}}} = 6.35$ cm,${T_{\rm{s}}} = 0.87$ s,$\theta = {0^\circ }$ ; c.${H_{\rm{s}}} = 3.59$ cm,${T_{\rm{s}}} = 0.8$ s,$\theta = {0^\circ }$ ; and d.${H_{\rm{s}}} = 3.59$ cm,${T_{\rm{s}}} = 0.8$ s,$\theta = - {22.5^\circ }$ .
Figure 11. The variation of freak factor
${H_{\rm{m}}}/{H_{\rm{s}}}$ (solid line), kurtosis (dot line) along the wave evolution. a.${H_{\rm{s}}} = 6.35$ cm at Probe G,$\theta = {0^ \circ }$ ; and b.${H_{\rm{s}}} = 3.59$ cm at Probe H,$\theta = {0^ \circ }$ .
Figure 12. The times variation of freak wave occurrence along the terrain (solid curve).
Table 1. Working conditions of irregular wave tests for 39 cases in terms of significant wave height
${H_{\rm{s}}}$ and significant period${T_{\rm{s}}}$ Case Wave
directions$(\theta )$ ${H_{\rm{s}}}$ /cm${T_{\rm{s}}}$ /sA1 ${22.5^\circ }$ 1.61 0.73 A2 3.59 0.73 A3 6.35 0.87 A4 8.05 0.87 A5 ${0^ \circ }$ 1.61 0.67, 0.73, 0.8, 0.87, 0.93, 1, 1.07, 1.2 A6 3.59 0.67, 0.73, 0.8, 0.87, 0.93, 1, 1.07, 1.14 A7 4.82 0.73 A8 6.35 0.8, 0.87, 0.93, 1, 1.07, 1.14, 1.21 A9 8.05 0.8, 0.87, 0.93, 1, 1.07, 1.14, 1.21 A10 $ - {22.5^\circ }$ 8.37 1.05 A11 1.71 0.65 A12 3.59 0.80 A13 7.08 0.91 
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