Phase saddles and dislocations in two-dimensional waves such as the tides
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 dislocati...
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Online Access: | http://dx.doi.org/10.1098/rspa.1988.0047 https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.1988.0047 |
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crroyalsociety:10.1098/rspa.1988.0047 2024-06-02T07:56:30+00:00 Phase saddles and dislocations in two-dimensional waves such as the tides 1988 http://dx.doi.org/10.1098/rspa.1988.0047 https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.1988.0047 en eng The Royal Society https://royalsociety.org/journals/ethics-policies/data-sharing-mining/ Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences volume 417, issue 1852, page 7-20 ISSN 0080-4630 journal-article 1988 crroyalsociety https://doi.org/10.1098/rspa.1988.0047 2024-05-07T14:16:47Z 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. Article in Journal/Newspaper Antarc* Antarctic Antarctic Peninsula The Royal Society Antarctic The Antarctic Antarctic Peninsula Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences 417 1852 7 20 |
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The Royal Society |
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English |
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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. |
format |
Article in Journal/Newspaper |
title |
Phase saddles and dislocations in two-dimensional waves such as the tides |
spellingShingle |
Phase saddles and dislocations in two-dimensional waves such as the tides |
title_short |
Phase saddles and dislocations in two-dimensional waves such as the tides |
title_full |
Phase saddles and dislocations in two-dimensional waves such as the tides |
title_fullStr |
Phase saddles and dislocations in two-dimensional waves such as the tides |
title_full_unstemmed |
Phase saddles and dislocations in two-dimensional waves such as the tides |
title_sort |
phase saddles and dislocations in two-dimensional waves such as the tides |
publisher |
The Royal Society |
publishDate |
1988 |
url |
http://dx.doi.org/10.1098/rspa.1988.0047 https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.1988.0047 |
geographic |
Antarctic The Antarctic Antarctic Peninsula |
geographic_facet |
Antarctic The Antarctic Antarctic Peninsula |
genre |
Antarc* Antarctic Antarctic Peninsula |
genre_facet |
Antarc* Antarctic Antarctic Peninsula |
op_source |
Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences volume 417, issue 1852, page 7-20 ISSN 0080-4630 |
op_rights |
https://royalsociety.org/journals/ethics-policies/data-sharing-mining/ |
op_doi |
https://doi.org/10.1098/rspa.1988.0047 |
container_title |
Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences |
container_volume |
417 |
container_issue |
1852 |
container_start_page |
7 |
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20 |
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1800756528840441856 |