Modelling wind waves. What lies beyond the significant wave height?

海洋中随机风浪的模拟是一个具有广泛应用意义的基础性问题。适当的海浪模型对于航海、渔业、近海工业、沿海环境管理至关重要；另一方面，融入天气和气候模型是海气相互作用的基础。至关重要的是，各种电磁频谱(包括卫星、机载、陆上和船基设备)中的所有海洋遥感都依赖于对风浪场特征的了解。提高这方面的知识将提高遥感能力。目前，所有的波模拟都是基于哈塞尔曼动力学方程(又名KE)及其修正。风浪是随机的，KE描述了由于非线性共振相互作用而引起的不同尺度和方向的海浪之间的能量交换以及风和耗散的能量输入所引起的集合平均量的演变。与光谱分量之间的能量重新分配有关的部分，S_NL，被认为是几十年来牢牢确立的，因为它与其他物理学分支一样，是从第一原理推导出来的。波浪模拟的总体情况不能被认为是令人满意的。尽管KE确实捕捉到了总体特征(峰值频率、有效波高)的行为，但KE模拟和高质量观测之间存在着无法解释的重大系统差异：观察到的光谱要宽得多，光谱峰值的幅度可能要小得多。该项目的本质和主要创新之处在于应用原始的直接数值模拟算法(DNS-ZE)来分析高质量数据：Romero和Melville(Tehuantepec实验)在墨西哥海岸外的独特观测以及D.Hauser使用机载和卫星散射计(Kuros和CFOSAT的SWIM)获得的观测数据。DNS-ZE是一种基于对非线性正则变量中欧拉方程的弱非线性化简进行积分的算法。目前，它是唯一能够模拟数百公里范围内海浪演变的域名系统代码。与DNS-ZE的模拟显示出与观测的良好一致性以及与KE预测的主要差异。该提议旨在利用DNS-ZE算法和新的高质量数据集(重新访问Tehuantepec观测并处理Kuros和游泳数据)的协同所带来的独特机会，并解决以下关键问题：(I)表明对于由高质量数据支持的各种波浪演变情景，DNS-ZE确实真实地捕捉到了演变。(Ii)恢复各种定常风条件下的源函数(风输入和风耗散)。(Iii)为了量化基于KE的预测的错误程度，研究对频谱形状敏感的具体含义，例如对于异常海浪的概率演变、上层海洋中的波浪诱导混合。(Iv)在寻找KE失败的原因方面取得进展。这项计划的实现将从根本上改变目前对海浪模拟准确性的理解和现有模型的严重局限性。在寻找KE失效原因方面的进展将不仅是对风浪的理解的突破，也是对流体和等离子体中各种随机非线性波的理解的突破。

Modelling random wind waves in the ocean is a fundamental problem with wide ranging applications of great significance. Proper wave modelling is crucial for navigation, fisheries, offshore industries, managing of coastal environments; on the other hand, being integrated into the weather and climate models it is fundamental for air-sea interaction. Crucially, all the ocean remote sensing in various bands of electromagnetic spectrum (including the satellite, airborne, on-shore and ship based devices) relies on knowledge of wind wave field characteristics. Improving this knowledge would increase remote sensing capabilities.Currently, all wave modelling is based on the Hasselmann kinetic equation, aka KE, and its modifications. Wind waves are random, and the KE describes evolution of ensemble averaged quantities caused by energy exchange between waves of different scales and directions owing to nonlinear resonant interactions, as well as energy input from wind and dissipation. The part concerned with the redistribution of energy between spectral components, S_nl, was considered to be firmly established for many decades, since it was derived from first principles in the same way as in other branches of physics.The overall situation in wave modelling cannot be considered satisfactory. Although the KE does capture the behaviour of bulk characteristics (peak frequency, significant wave height) there are unexplained major systematic discrepancies between the KE modelling and the high quality observations: the observed spectra are much wider and the magnitude of the spectral peak could be considerably smaller.The essence and main novelty of the project is in applying original direct numerical simulations algorithm (DNS-ZE) to analyse high quality data: unique observations off the Mexican coast by Romero & Melville (the Tehuantepec experiment) and data from observations by D.Hauser obtained using airborne and satellite scatterometers (KuROS and SWIM of CFOSAT). The DNS-ZE is an algorithm based on integration of a weakly nonlinear reduction of the Euler equations in nonlinear canonical variables. Currently it is the only DNS code able to perform simulations of wave evolution over several hundred kilometers. The simulations with the DNS-ZE showed excellent agreement with the observations and major discrepancies with the KE predictions.The proposal aims to utilise the unique opportunities opened by synergy of the DNS-ZE algorithm and new high quality datasets (revisited Tehuantepec observations and processed KuROS and SWIM data) and to address the following key problems:(i) To show that for various wave evolution scenarios supported by high quality data, the DNS-ZE indeed faithfully captures the evolution.(ii) To retrieve the source functions (wind input and dissipation) for various steady wind conditions.(iii) To quantify how wrong are the KE based predictions, to examine the specific implications sensitive to the shape of the spectra, e.g. for evolution of probability of freak waves, wave induced mixing in the upper ocean.(iv) To advance in finding the cause of the KE failure.The realisation of this project would change radically the present understanding of the accuracy of wave modelling and the serious limitations of the existing models. Advance in finding the cause of the KE failure would be a breakthrough in understanding of not only wind waves, but all kind of random nonlinear waves in fluids and plasmas.