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
Main Authors: Borzi, C H, Kraenkel, R A, Manna, M A, Pereira, A
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Language:English
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Nonlinear Sciences
Pattern Formation and Solitons
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description 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.
doi_str_mv 10.1103/PhysRevE.71.026307
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subjects Nonlinear Sciences
Pattern Formation and Solitons
title Nonlinear dynamics of short traveling capillary-gravity waves
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