Hamiltonian Dysthe equation for 3D deep-water gravity waves
Analysis of PDEs
2021-08-25 v1
Abstract
This article concerns the water wave problem in a three-dimensional domain of infinite depth and examines the modulational regime for weakly nonlinear wavetrains. We use the method of normal form transformations near the equilibrium state to provide a new derivation of the Hamiltonian Dysthe equation describing the slow evolution of the wave envelope. A precise calculation of the third-order normal form allows for a refined reconstruction of the free surface. We test our approximation against direct numerical simulations of the three-dimensional Euler system and against predictions from the classical Dysthe equation, and find very good agreement.
Keywords
Cite
@article{arxiv.2108.10822,
title = {Hamiltonian Dysthe equation for 3D deep-water gravity waves},
author = {Philippe Guyenne and Adilbek Kairzhan and Catherine Sulem},
journal= {arXiv preprint arXiv:2108.10822},
year = {2021}
}