五阶双色双向海洋表面波理论

A 5th-Order Theory for Bichromatic and Bidirectional Ocean Surface Waves

将经典的"纯波动的三阶单色单向Stokes波理论"提升至"可包含环境均匀流效应的有限水深五阶双色双向海洋表面波理论".亦即,在已有三阶双色双波理论的基础上得到了自由表面位移、速度势和非线性振幅色散关系的第四阶、第五阶显式表达式.从中,将居于核心地位的"双色双向波的第五阶非线性振幅色散关系"又推广到"无穷多波中任意两两不同频率不同振幅相互作用波的非线性振幅色散关系".针对双色双向短峰波的典型特性,以若干个图表详加示之.

The classical Stokes wave theory of pure wave motion for the 3rd-order monochro- matic and monodirectional waves was expanded to a 5th-order theory for bichromatic and bidi- rectional ocean surface waves under the ambient uniform current effect in water of finite depth, which, based on the 3rd-order theory for bichromatic and bidirectional waves, comprised the 4th- and the 5th-order explicit expressions for the free surface elevations, the velocity potential and the nonlinear amplitude dispersion relation. The 5th-order nonlinear amplitude dispersion relation playing a key role in the bichromatic and bidirectional wave theory was generalized to one relation of 2 arbitrary interacting waves with different frequencies and ampitudes in pairs out of infinite waves. The typical characteristics of bichromatic and bidirectional short-crested waves were illustrated in detail with diagrams.