Physics – Fluid Dynamics
Scientific paper
2010-05-30
Commun Nonlinear Sci Numer Simulat 16 (2011) 1274-1303
Physics
Fluid Dynamics
50 pages, 11 figures
Scientific paper
10.1016/j.cnsns.2010.06.026
The basic ideas of a homotopy-based multiple-variable method is proposed and applied to investigate the nonlinear interactions of periodic traveling waves. Mathematically, this method does not depend upon any small physical parameters at all and thus is more general than the traditional multiple-scale perturbation techniques. Physically, it is found that, for a fully developed wave system, the amplitudes of all wave components are finite even if the wave resonance condition given by Phillips (1960) is exactly satisfied. Besides, it is revealed that there exist multiple resonant waves, and that the amplitudes of resonant wave may be much smaller than those of primary waves so that the resonant waves sometimes contain rather small part of wave energy. Furthermore, a wave resonance condition for arbitrary numbers of traveling waves with large wave amplitudes is given, which logically contains Phillips' four-wave resonance condition but opens a way to investigate the strongly nonlinear interaction of more than four traveling waves with large amplitudes. This work also illustrates that the homotopy multiple-variable method is helpful to gain solutions with important physical meanings of nonlinear problems, if the multiple variables are properly defined with clear physical meanings.
No associations
LandOfFree
On the homotopy multiple-variable method and its applications in the interactions of nonlinear gravity waves does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On the homotopy multiple-variable method and its applications in the interactions of nonlinear gravity waves, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the homotopy multiple-variable method and its applications in the interactions of nonlinear gravity waves will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-162065