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Evolution of ocean wave statistics in shallow water: Refraction and diffraction over seafloor topography

機(jī)譯：淺海海浪統(tǒng)計(jì)的演變：海底地形的折射和衍射

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摘要

We present a stochastic model for the evolution of random ocean surface waves in coastal waters with complex seafloor topography. First, we derive a deterministic coupled-mode model based on a forward scattering approximation of the nonlinear mild slope equation; this model describes the evolution of random, directionally spread waves over fully two-dimensional topography, while accounting for wide angle refraction/diffraction, and quadratic nonlinear coupling. On the basis of the deterministic evolution equations, we derive transport equations for the wave statistical moments. This stochastic model evolves the complete wave cross-correlation matrix and thus resolves spatially coherent wave interference patterns induced by topographic scattering as well as nonlinear energy transfers to higher and lower frequencies. In this paper we focus on the linear aspects of the interaction with seafloor topography. Comparison to analytic solutions and laboratory observations confirms that (1) the forward scattering approximation is suitable for realistic two-dimensional topography, and (2) the combined effects of wide angle refraction and diffraction are accurately captured by the stochastic model.
機(jī)譯：我們提出了隨機(jī)海面波在具有復(fù)雜海底地形的沿海水域中演化的隨機(jī)模型。首先，我們基于非線性溫和斜率方程的前向散射近似推導(dǎo)確定性耦合模式模型。該模型描述了在完全二維地形上隨機(jī)定向分布波的演化，同時(shí)考慮了廣角折射/衍射和二次非線性耦合。在確定性演化方程的基礎(chǔ)上，我們推導(dǎo)出了波浪統(tǒng)計(jì)矩的傳輸方程。該隨機(jī)模型演化出完整的波互相關(guān)矩陣，從而解決了由地形散射以及非線性能量傳遞到更高和更低頻率所引起的空間相干波干涉圖。在本文中，我們關(guān)注與海底地形相互作用的線性方面。與分析解決方案和實(shí)驗(yàn)室觀察結(jié)果的比較證實(shí)，（1）正向散射近似適用于逼真的二維地形，并且（2）隨機(jī)模型可以準(zhǔn)確捕獲廣角折射和衍射的組合效應(yīng)。

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