Nonlinear random wave field in shallow water: variable Korteweg-de Vries framework
The transformation of a random wave field in shallow water of variable depth is analyzed within the framework of the variable-coefficient Korteweg-de Vries equation. The characteristic wave height varies with depth according to Green's law, and this follows rigorously from the theoretical model...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Copernicus Publications
2011-02-01
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| Series: | Natural Hazards and Earth System Sciences |
| Online Access: | http://www.nat-hazards-earth-syst-sci.net/11/323/2011/nhess-11-323-2011.pdf |
| _version_ | 1828412089953157120 |
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| author | A. Sergeeva E. Pelinovsky T. Talipova |
| author_facet | A. Sergeeva E. Pelinovsky T. Talipova |
| author_sort | A. Sergeeva |
| collection | DOAJ |
| description | The transformation of a random wave field in shallow water of variable depth is analyzed within the framework of the variable-coefficient Korteweg-de Vries equation. The characteristic wave height varies with depth according to Green's law, and this follows rigorously from the theoretical model. The skewness and kurtosis are computed, and it is shown that they increase when the depth decreases, and simultaneously the wave state deviates from the Gaussian. The probability of large-amplitude (rogue) waves increases within the transition zone. The characteristics of this process depend on the wave steepness, which is characterized in terms of the Ursell parameter. The results obtained show that the number of rogue waves may deviate significantly from the value expected for a flat bottom of a given depth. If the random wave field is represented as a soliton gas, the probabilities of soliton amplitudes increase to a high-amplitude range and the number of large-amplitude (rogue) solitons increases when the water shallows. |
| first_indexed | 2024-12-10T12:42:54Z |
| format | Article |
| id | doaj.art-e916abfc1d5f4046a0a02dea32bf1fa2 |
| institution | Directory Open Access Journal |
| issn | 1561-8633 1684-9981 |
| language | English |
| last_indexed | 2024-12-10T12:42:54Z |
| publishDate | 2011-02-01 |
| publisher | Copernicus Publications |
| record_format | Article |
| series | Natural Hazards and Earth System Sciences |
| spelling | doaj.art-e916abfc1d5f4046a0a02dea32bf1fa22022-12-22T01:48:30ZengCopernicus PublicationsNatural Hazards and Earth System Sciences1561-86331684-99812011-02-0111232333010.5194/nhess-11-323-2011Nonlinear random wave field in shallow water: variable Korteweg-de Vries frameworkA. SergeevaE. PelinovskyT. TalipovaThe transformation of a random wave field in shallow water of variable depth is analyzed within the framework of the variable-coefficient Korteweg-de Vries equation. The characteristic wave height varies with depth according to Green's law, and this follows rigorously from the theoretical model. The skewness and kurtosis are computed, and it is shown that they increase when the depth decreases, and simultaneously the wave state deviates from the Gaussian. The probability of large-amplitude (rogue) waves increases within the transition zone. The characteristics of this process depend on the wave steepness, which is characterized in terms of the Ursell parameter. The results obtained show that the number of rogue waves may deviate significantly from the value expected for a flat bottom of a given depth. If the random wave field is represented as a soliton gas, the probabilities of soliton amplitudes increase to a high-amplitude range and the number of large-amplitude (rogue) solitons increases when the water shallows.http://www.nat-hazards-earth-syst-sci.net/11/323/2011/nhess-11-323-2011.pdf |
| spellingShingle | A. Sergeeva E. Pelinovsky T. Talipova Nonlinear random wave field in shallow water: variable Korteweg-de Vries framework Natural Hazards and Earth System Sciences |
| title | Nonlinear random wave field in shallow water: variable Korteweg-de Vries framework |
| title_full | Nonlinear random wave field in shallow water: variable Korteweg-de Vries framework |
| title_fullStr | Nonlinear random wave field in shallow water: variable Korteweg-de Vries framework |
| title_full_unstemmed | Nonlinear random wave field in shallow water: variable Korteweg-de Vries framework |
| title_short | Nonlinear random wave field in shallow water: variable Korteweg-de Vries framework |
| title_sort | nonlinear random wave field in shallow water variable korteweg de vries framework |
| url | http://www.nat-hazards-earth-syst-sci.net/11/323/2011/nhess-11-323-2011.pdf |
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