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Nonlinear dynamics of short traveling capillary-gravity waves
We establish a Green-Nagdhi model equation for capillary-gravity waves in (2+1) dimensions. Through the derivation of an asymptotic equation governing short-wave dynamics, we show that this system possesses (1+1) traveling-wave solutions for almost all the values of the Bond number theta (the specia...
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Published in: | Physical review. E, Statistical, nonlinear, and soft matter physics Statistical, nonlinear, and soft matter physics, 2005-02, Vol.71 (2 Pt 2), p.026307-026307, Article 026307 |
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Main Authors: | , , , |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that this one cites Items that cite this one |
Online Access: | Get full text |
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Summary: | We establish a Green-Nagdhi model equation for capillary-gravity waves in (2+1) dimensions. Through the derivation of an asymptotic equation governing short-wave dynamics, we show that this system possesses (1+1) traveling-wave solutions for almost all the values of the Bond number theta (the special case theta=1/3 is not studied). These waves become singular when their amplitude is larger than a threshold value, related to the velocity of the wave. The limit angle at the crest is then calculated. The stability of a wave train is also studied via a Benjamin-Feir modulational analysis. |
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ISSN: | 1539-3755 1550-2376 |
DOI: | 10.1103/PhysRevE.71.026307 |