Ocean swell plays an important role in the transport of energy across the ocean, yet its evolution is not well understood. In the late 1960s, the nonlinear Schrödinger (NLS) equation was derived as a simplified model for the propagation of ocean swell over large distances. More recently, a number of dissipative generalizations of the NLS equation based on a simple dissipation assumption have been proposed. These models have been shown to accurately model wave evolution in a laboratory setting, but their validity in modeling ocean swell has not previously been examined. We study the efficacy of the NLS equation and four of its generalizations in modeling the evolution of swell in the ocean. The dissipative models perform significantly better than conservative ones and are overall reasonable models for swell amplitudes, indicating dissipation is an important physical effect in ocean swell evolution. The nonlinear models did not outperform their linearizations, indicating linear models may be sufficient in modeling some aspects of ocean swell evolution over large distances.

中文翻译：

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太平洋涌浪传播的耗散模型

海涌在跨洋能量传输中发挥着重要作用，但其演变过程尚不清楚。在 1960 年代后期，非线性薛定谔 (NLS) 方程被推导出为海洋膨胀远距离传播的简化模型。最近，已经提出了许多基于简单耗散假设的 NLS 方程的耗散推广。这些模型已被证明可以在实验室环境中准确地模拟波浪演化，但它们在模拟海浪中的有效性之前尚未得到检验。我们研究了 NLS 方程及其四个推广在模拟海洋涌浪演变过程中的有效性。耗散模型的性能明显优于保守模型，并且是膨胀幅度的总体合理模型，表明耗散是海浪演化中的一个重要物理效应。非线性模型的表现并不优于其线性化，这表明线性模型可能足以模拟远距离海浪演化的某些方面。