In freak wave-related research, the wavelength of the freak wave is generally calculated from the dispersion relation of the Stokes wave or linear wave. The freak wave, however, is a type of short-duration wave, also characterized by strong-nonlinearity. Its energy components are more complex compared to regular waves. Beside the effect of higher-order harmonics, the energy transfer occurs due to the nonlinear wave-wave interaction during the generation of freak waves. In order to check the accuracy of the wavelength of freak waves calculated from the dispersion relation, freak waves were experimentally simulated in a wave tank by focusing a range of component waves. The statistics on wavelength of freak wave were calculated from the time history of wave surface obtained from a wave gauge array. The statistical wavelengths conduted were compared to those of linear wave, 3rd- and 5th-order Stokes wave with identical wave heights and periods. The results from comparison indicate that the wavelengths from the 3rd- and 5th-order Stokes wave dispersion relations have a higher accuracy than that from the 1st-order dispersion relations of linear wave. And the 3rd-order dispersion relation is sufficient to describe the effect of higher-order harmonics on the wavelength. However, without accounting for the nonlinear wave-wave interaction, high-order dispersion relation will overestimate the wavelength of frear wave with longer periods and underestimate that for freak wave with shorter periods. And as a consequence, on the basis of the 3rd-order dispersion relation and regression model, a new improved method for higher accuracy calculation of the wavelengths of the freak wave was proposed. The accuracy of the wavelengths for the new method increases by over 50% compared to the tradional 3rd-order dispersion relation.
| 科 Family | 属数 Number of genus | 种数 Number of species | 占总种数比例 Percentage of total species (%) | 属 Genus | 种数 Number of species | 占总种数比例 Percentage of total species (%) |
|---|---|---|---|---|---|---|
| 鹅膏菌科Amanitaceae | 2 | 11 | 5.26 | 鹅膏菌属 Amanita | 10 | 4.78 |
| 小菇科 Mycenaceae | 2 | 12 | 5.74 | 丝盖伞属 Inocybe | 5 | 2.39 |
| 多孔菌科 Polyporaceae | 8 | 14 | 6.70 | 蜡蘑属 Laccaria | 5 | 2.39 |
| 红菇科 Russulaceae | 3 | 23 | 11.00 | 小皮伞属 Marasmius | 6 | 2.87 |
| 小菇属 Mycena | 11 | 5.26 | ||||
| 光柄菇属 Pluteus | 5 | 2.39 | ||||
| 红菇属 Russula | 17 | 8.13 | ||||
| 栓菌属 Trametes | 5 | 2.39 |