Investigation of the maximum amplitude increase from the Benjamin-Feir instability
Fluid Dynamics
2011-10-25 v1
Abstract
The Nonlinear Schr\"odinger (NLS) equation is used to model surface waves in wave tanks of hydrodynamic laboratories. Analysis of the linearized NLS equation shows that its harmonic solutions with a small amplitude modulation have a tendency to grow exponentially due to the so-called Benjamin-Feir instability. To investigate this growth in detail, we relate the linearized solution of the NLS equation to a fully nonlinear, exact solution, called soliton on finite background. As a result, we find that in the range of instability the maximum amplitude increase is finite and can be at most three times the initial amplitude.
Keywords
Cite
@article{arxiv.1110.4686,
title = {Investigation of the maximum amplitude increase from the Benjamin-Feir instability},
author = {N. Karjanto and E. van Groesen and P. Peterson},
journal= {arXiv preprint arXiv:1110.4686},
year = {2011}
}
Comments
9 pages, 4 figures, presented in IAMS-Netherlands Seminar 2002