The Most Unstable Conditions of Modulation Instability
Modulation instability is one of the most ubiquitous types of instabilities in nature. As one of the key characteristics of modulation instability, the most unstable condition attracts lots of attention. The most unstable condition is investigated here with two kinds of initial wave systems via a nu...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/656873 |
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| author | Aifeng Tao Jinhai Zheng Soe Mee Mee Botao Chen |
| author_facet | Aifeng Tao Jinhai Zheng Soe Mee Mee Botao Chen |
| author_sort | Aifeng Tao |
| collection | DOAJ |
| description | Modulation instability is one of the most ubiquitous types of instabilities in nature. As one of the key characteristics of modulation instability, the most unstable condition attracts lots of attention. The most unstable condition is investigated here with two kinds of initial wave systems via a numerical high-order spectral method (HOS) for surface water wave field. Classically, one carrier wave and a pair of sidebands are implied as the first kind of initial wave system: “seeded” wave system. In the second kind of initial wave system: “un-seeded” wave system, only one carrier wave is implied. Two impressive new results are present. One result shows that the grow rates of lower and upper sideband are different within the “seeded” wave system. It means that, for a given wave steepness, the most unstable lower sideband is not in pair with the most unstable upper sideband. Another result shows the fastest growing sidebands are exactly in pair from “unseeded” wave system. And the most unstable conditions of “unseeded” wave system are more or less the mean value of those derived from the lower sidebands and upper sidebands within the “seeded” wave system. |
| format | Article |
| id | doaj-art-f8d8d7d6063545288415cd9dad04c26e |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-f8d8d7d6063545288415cd9dad04c26e2025-02-03T01:30:55ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/656873656873The Most Unstable Conditions of Modulation InstabilityAifeng Tao0Jinhai Zheng1Soe Mee Mee2Botao Chen3Key Laboratory of Coastal Disaster and Defence of Ministry of Education, Hohai University, Nanjing 210098, ChinaCollege of Harbor, Coastal and Offshore Engineering, Hohai University, Nanjing 210098, ChinaDepartment of Port & Harbour Engineering, Myanmar Maritime University, Yangon 11000, MyanmarCollege of Harbor, Coastal and Offshore Engineering, Hohai University, Nanjing 210098, ChinaModulation instability is one of the most ubiquitous types of instabilities in nature. As one of the key characteristics of modulation instability, the most unstable condition attracts lots of attention. The most unstable condition is investigated here with two kinds of initial wave systems via a numerical high-order spectral method (HOS) for surface water wave field. Classically, one carrier wave and a pair of sidebands are implied as the first kind of initial wave system: “seeded” wave system. In the second kind of initial wave system: “un-seeded” wave system, only one carrier wave is implied. Two impressive new results are present. One result shows that the grow rates of lower and upper sideband are different within the “seeded” wave system. It means that, for a given wave steepness, the most unstable lower sideband is not in pair with the most unstable upper sideband. Another result shows the fastest growing sidebands are exactly in pair from “unseeded” wave system. And the most unstable conditions of “unseeded” wave system are more or less the mean value of those derived from the lower sidebands and upper sidebands within the “seeded” wave system.http://dx.doi.org/10.1155/2012/656873 |
| spellingShingle | Aifeng Tao Jinhai Zheng Soe Mee Mee Botao Chen The Most Unstable Conditions of Modulation Instability Journal of Applied Mathematics |
| title | The Most Unstable Conditions of Modulation Instability |
| title_full | The Most Unstable Conditions of Modulation Instability |
| title_fullStr | The Most Unstable Conditions of Modulation Instability |
| title_full_unstemmed | The Most Unstable Conditions of Modulation Instability |
| title_short | The Most Unstable Conditions of Modulation Instability |
| title_sort | most unstable conditions of modulation instability |
| url | http://dx.doi.org/10.1155/2012/656873 |
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