Hamiltonian Dysthe Equation for Three-Dimensional Deep-Water Gravity Waves
Date
2022-03-17
Journal Title
Journal ISSN
Volume Title
Publisher
Multiscale Modeling and Simulation
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.
Description
This article was originally published in Multiscale Modeling and Simulation. The version of record is available at: https://doi.org/10.1137/21M1432788
Keywords
three-dimensional deep-water waves, Hamiltonian systems, normal form transformations, modulational analysis, Dysthe equation, numerical simulations
Citation
Guyenne, Philippe, Adilbek Kairzhan, and Catherine Sulem. “Hamiltonian Dysthe Equation for Three-Dimensional Deep-Water Gravity Waves.” Multiscale Modeling & Simulation 20, no. 1 (2022): 349–78. https://doi.org/10.1137/21M1432788.