A theoretical and computational study is undertaken for the modulational instabilities of a pair of nonlinearly interacting two-dimensional waves in deep water. It has been shown that the full dynamics of these interacting waves gives rise to localized large-amplitude wavepackets (wave focusing). The coupled cubic nonlinear Schrödinger (CNLS) equations are used to derive a nonlinear dispersion equation which give rise to new class of modulational instabilities and demonstrates the dependence of obliqueness of the interacting waves. The computations, due to nonlinear wave-wave interactions, waves that are separately modulationally stable can give rise to the formation of large-amplitude coherent wave packets with amplitudes several times that of the initial waves. In the case for the original Benjamin-Feir instability, in constrast, waves disintegrate into a wide spectrum.
Proceedings of the 11th International Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE
Number of Pages
Scholarly Commons Citation
Khanal, H., Mancas, S., & Sajjadi, S. (2011). Interactions and Focusing of Nonlinear Water Waves. , (). Retrieved from https://commons.erau.edu/publication/780