论文标题
哈密顿的dysthe方程，用于恒定涡流的深水重力波
A Hamiltonian Dysthe equation for deep-water gravity waves with constant vorticity
论文作者
论文摘要
本文是对在非零恒定涡度存在下无限深度的二维结构域中水浪问题的研究。一个目的是描述均匀剪切流对弱非线性准单色表面重力波的调节的影响。从哈密顿的该问题的表述和使用哈密顿转化理论的技术开始，我们在波封膜的时间演变中得出了哈密顿的dysthe方程。与以前的研究一致，我们观察到均匀的剪切流往往会根据其方向和强度增强或削弱Stokes波的模稳定性。我们的方法还提供了一种非扰动程序，以基于Birkhoff的正常形式转换来重建从波包膜的表面抬高以消除所有非谐波三合会。该模型是针对整个Euler方程的直接数值模拟进行了测试的，以及在恒定涡度的背景下，Curtis，Carter和Kalisch最近得出的相关dysthe方程（J. Fluid Mech。855，2018）。对于一系列涡度值，发现非常好的一致性。
This paper is a study of the water wave problem in a two-dimensional domain of infinite depth in the presence of nonzero constant vorticity. A goal is to describe the effects of uniform shear flow on the modulation of weakly nonlinear quasi-monochromatic surface gravity waves. Starting from the Hamiltonian formulation of this problem and using techniques from Hamiltonian transformation theory, we derive a Hamiltonian Dysthe equation for the time evolution of the wave envelope. Consistent with previous studies, we observe that the uniform shear flow tends to enhance or weaken the modulational instability of Stokes waves depending on its direction and strength. Our method also provides a non-perturbative procedure to reconstruct the surface elevation from the wave envelope, based on the Birkhoff normal form transformation to eliminate all non-resonant triads. This model is tested against direct numerical simulations of the full Euler equations and against a related Dysthe equation recently derived by Curtis, Carter and Kalisch (J. Fluid Mech. 855, 2018) in the context of constant vorticity. Very good agreement is found for a range of values of the vorticity.
