三阶表面张力-重力短峰波理论

Third-Order Theory for Surface Capillary-Gravity Short-Crested Waves

考虑作用于表面波上的丰富表面张力效应,构造有限水深表面张力-重力短峰波系统,提出其解的唯一性条件,并获得其三阶解析解.据此,给出一系列与近海、海洋工程密切相关的运动学、动力学变量表达式:自由表面位移、速度势、角频率、波陡、相速度、水质点速度和加速度、波压力.并且发现,三阶角频率的零点、极点直接关系到谐波共振.

Considering the rich capillary effects on surface waves,a system for surface capillary-gravity short-crested waves is developed.The unique solution condition is given,and the third-order solution obtained,leading to expressions for a series of kinematic and dynamic variables closely related to coastal and ocean engineering.These expressions deal with surface elevation,velocity potential,angular frequency,wave steepness,phase velocity,wave-particle velocities and accelerations,and wave pressure.It is found that locations of zeros and poles of the third-order angular frequency directly correspond to the harmonic resonances.