Phase saddles and dislocations in two-dimensional waves such as the tides
Phase saddles and dislocations in two-dimensional waves such as the tides
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潮汐等二维波中的相鞍和位错
DOI：
10.1098/rspa.1988.0047
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发表时间：
1988
期刊：
影响因子：
--
通讯作者：
J. Hannay
中科院分区：
文献类型：
--
作者：
J. Nye;J. Hajnal;J. Hannay
固定频率的二维标量波场通常包含振幅为零且相位不确定的点。在等相位等高线图上，这些波位错（干涉零点）伴有鞍。当一个外部参数改变时，位错可以成对产生，也可以成对相遇并相互破坏。对于最简单的单频波动方程，在拓扑上必须有两个鞍点参与这一事件；而且，在湮灭前的最后阶段，它们必须位于直径为位错连接线的圆上。文中给出了一些例子，说明即使最初的配置非常不同，也总是最终达到这种基本模式。在潮汐理论中，位错是两相点，移动它们的外部参数可以是频率。湮灭事件的一个例子发生在南大西洋，一对紧密的双角点可以解释南极半岛的异常潮汐观测。与潮汐涨落不同，潮流提供了一个二维或三维矢量场的例子，并指出该场中的奇点与电磁波极化场中的奇点完全相同。
A two-dimensional scalar wavefield of fixed frequency contains, in general, points where the amplitude is zero and the phase is indeterminate. On a map of contours of equal phase these wave dislocations (interference nulls) are accompanied by saddles. When an external parameter is changed dislocations can be created in pairs or a pair can meet and destroy one another. For the simplest single-frequency wave equation it is a topological necessity that two saddles should participate in this event; moreover, they have to lie, in the final stage before annihilation, on the circle whose diameter is the line joining the dislocations. Examples are given to show how this basic pattern is always ultimately attained even when initially the configuration is quite different. In tidal theory, where the dislocations are amphidromic points, the external parameter that moves them can be the frequency. An example of an annihilation event occurs in the South Atlantic, and a close pair of amphidromic points may explain anomalous tidal observations from the Antarctic Peninsula. The tidal current, as distinct from the tidal rise and fall, provides an example of a two or three-dimensional vector field, and it is pointed out that the singularities in this field are precisely the same as those to be found in the polarization field of an electromagnetic wave.