波群的波向线方程  

RAY EQUATIONS FOR OCEAN WAVE GROUPS

作　　者：汪炳祥[1] 

机构地区：[1]物理海洋学与海洋气象学系

出　　处：《山东海洋学院学报》1986年第3期1-14,共14页

摘　　要：海浪传入浅水域后发生的折射，是影响该海域的波动状态的重要因素之一，从而关系到船舰在大陆架航行的安全，关系到近海和近岸海洋工程的选址及其结构物的设计，关系到海岸线和海滩的演变，所以日益引起海洋学界和海洋工程学界的注意和讨论。In the present paper a new geometric group velocity is proposed, and to avoid confusion, here it is temporarily termed the general geometric group velocity. The ray equations for a wave group, which is obtained by the addition of two sine gravity water waves with equal amplitudes of slighly different wave numbers, frequencies, and propagation directions with respect to the positive X axis, are derived in both the plane Cartesian coordinates and the spherical coordinates based on Fermat's principle.The ray curvature for the trajectory of the group on the plane coordinates is a function of such characteristics of the components as phase velocities, periods, and propagation directions;that on the spherical surface, besides the above three parameters, also contains thelatitude of the earth.As the wave components of unchanged but non-equal periods propagate at the same direction with equal celerities, the proposed equations are thereby reduced to that for a monochromatic wave on the corresponding coordinates.In a shallow water of uniform depth, the paths of the wave packet and the monochromatic wave on both the plane coordinates and the spherical coordinates completely resemble each other in shape.The properties of collineaf, geometric and general group velocity and the distinctions between them are explained by processes of numerical calculation.It has been shown that both the conventional group velocity and Breedo ing's geometric group velocity are only a particular case of the general geometric group velocity proposed by this paper.The chief objections to Breeding's geometric group velocity and reference are pointed out.

关 键 词：波群 波向线方程 海浪折射 波动状态 图解法 

分 类 号：P731.22[天文地球—海洋科学]