发表机构
CEA（法国原子能和替代能源委员会）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对空间尺度相当的深水表面重力波与背景流，推导了包含非线性波-波相互作用的双向耦合模型，并验证了守恒性质，为高效数值模拟提供了基础。
AI 中文摘要
我们考虑在背景流上方传播的窄带深水表面重力波，背景流的空间尺度与波长相当。我们关注背景流速度与波的斯托克斯漂移速度相当的参数区间，以推导快速波与慢速背景流之间的双向耦合模型。非线性波相互作用与双向耦合出现在相同的渐近阶数上，因此必须在推导中予以包含。所得模型由第一部分中得到的约化波动方程的非线性版本组成，并与控制背景流演化的克雷克-莱博维奇方程相耦合。该模型描述了波场和背景流在背景流的慢周转频率上的演化，从而节省了在时间上解析快速波频率的计算负担。无粘模型精确守恒波作用量、机械能和水平动量，而粘性模型精确守恒水平动量。耦合项以紧凑形式给出，便于物理解释和数值实现。
英文摘要
We consider narrow-band deep-water surface gravity waves propagating above a background flow whose spatial scale is comparable to the wavelength. We focus on the regime where the background-flow speed is comparable to the Stokes drift of the waves to derive a two-way coupled model between the fast waves and the slow background flow. Nonlinear wave interactions arise at the same asymptotic order as the two-way coupling and must therefore be included in the derivation. The resulting model consists of a nonlinear version of the reduced wave equation obtained in part I, coupled to a Craik-Leibovich equation governing the evolution of the background flow. The model describes the evolution of the wave field and background flow over the slow turnover frequency of the background flow, thus saving the computational burden of temporally resolving the fast wave frequency. The inviscid model exactly conserves wave action, mechanical energy and horizontal momentum, while the viscous model exactly conserves horizontal momentum. The coupling terms are cast in compact form for ease of physical interpretation and numerical implementation.
