Focusing of unidirectional wave groups on deep water: an approximate nonlinear Schrödinger equation-based model
Focusing of unidirectional wave groups on deep water: an approximate nonlinear Schrödinger equation-based model
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DOI：
10.1098/rspa.2009.0224
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发表时间：
2009-10
期刊：
影响因子：
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通讯作者：
T. Adcock;P. Taylor
中科院分区：
文献类型：
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作者：
T. Adcock;P. Taylor
本文提出了一个描述深水中高斯波群非线性演化的近似解析模型。该模型由立方非线性薛定谔方程(NLSE)的守恒量导出。描述这一演化的关键参数是振幅与波数带宽之比，这一数值类似于随机海态的本杰明-费尔指数。对于较小的这个参数，群是完全色散的，而对于更多的非线性情况，形成了孤子。我们的模型预测了两个政权中群体的特征和演变。这些预测结果与NLSE数值模拟结果吻合较好，与完全非线性势流解算器的数值结果和实验结果定性一致。
This paper sets out an approximate analytical model describing the nonlinear evolution of a Gaussian wave group in deep water. The model is derived using the conserved quantities of the cubic nonlinear Schrödinger equation (NLSE). The key parameter for describing the evolution is the amplitude-to-wavenumber bandwidth ratio, a quantity analogous to the Benjamin–Feir index for random sea-states. For smaller values of this parameter, the group is wholly dispersive, whereas for more nonlinear cases, solitons are formed. Our model predicts the characteristics and the evolution of the groups in both regimes. These predictions are found to be in good agreement with numerical simulations using the NLSE and are in qualitative agreement with numerical results from a fully nonlinear potential flow solver and experimental results.