New kinetic equations and their modelling for wind wave forecasting.

风浪是海洋/大气相互作用反馈回路中的关键环节。由于风浪控制着动量、气体和热交换的通量，风浪模拟的质量直接影响到天气预报的质量和对空气/水界面所有过程的描述的准确性。更好的风浪模型，特别是对“无赖”海浪的模拟，对于日益增长的航运和海上活动的可靠性确实至关重要。目前所有的波浪预报和模拟都是基于运动方程(KE)的数值积分，该方程也被称为哈塞尔曼方程。该方程考虑了风的输入、耗散以及不同尺度和方向的海浪之间的相互作用，描述了风浪谱在时间和空间上的缓慢演化。相互作用项，通常表示为SNL，在载能波中占主导地位。SNL的表达已经有半个世纪没有变化了。现在，观测质量的提高和用于波浪模拟的数据输入使人们不可能忽视以知识为基础的模型和观测之间的差异无法以任何方式弥合的情况。基于现有动力学方程的模型的以下基本缺陷变得明显：(I)通过构造，KE不能描述波场对快速扰动(例如，风的突然变化、阵风、尖锐边界等)的反应。(Ii)基于KE的模型只能预测波谱的演变，而非常需要模拟波高概率密度函数的演变，或者更准确地说，它偏离高斯分布。这对于预报流氓海浪，以及评估基于KE的模型的有效性尤其是非常必要的。KE本身并不知道它何时不再适用。为了解决这些缺点，作者最近提出了以下激进的想法。从第一原理出发，提出了两个最具限制性的假设：波场接近平衡，以及在考虑波场偏离高斯性时过于简化，从而导出了新的广义动力学方程。更重要的是，作者还发现，对于一个典型的风浪，一旦找到谱，就有可能重建概率密度函数的演化。该建议旨在通过阐述上述思想，建立一个新的研究风浪演变的数值和概念框架，并根据第一原理推导出的SNL的新表达式，开发一种新的风浪模拟方法。这个建议的目的是创建一个数值工具(稳健的并行代码)来求解新的动力学方程，然后使用这个工具来解决波场演化的突出问题。在开发程序时，我们将得到作者开发的用于模拟波场长时间演化的直接数值模拟算法的极大帮助。该算法将用于新代码的验证。在新工具的帮助下，我们将划定标准KE确实有效和不再适用的情况，并将调查远远超出其适用范围的波浪演变模式(例如阵风)。我们将模拟波场偏离高斯的演化，这将特别使评估反常波的概率成为可能。我们将为海浪预报制定“实用的”参数和建议。该项目旨在彻底改变风浪模型和预报。我们提出的新方法更适合于模拟的并行化和计算机计算能力的提高，最终将取代现有的计算SNL的算法。它不仅将更准确地描述现实，而且还有可能更快地实现这一点。

Wind waves are a key link in the feedback loop of ocean/atmosphere interaction. The quality of wind wave modelling directly affects the quality of weather forecasting and the accuracy of description of all processes at the air/water interface, since waves control fluxes of momentum, gas and heat exchange. Better wind wave modelling, especially of 'rogue' waves, is literally vital for reliability of growing shipping and offshore activities. At present all wave forecasting and modelling is based on numerical integration of the kinetic equation (KE), which is also referred to as the Hasselmann equation. The equation takes into account wind input, dissipation and interaction between waves of different scales and directions and describes the slow evolution of wind wave spectra in time and space. The interaction term, usually denoted as Snl, is dominant for energy carrying waves. The expression for Snl has not changed for half a century. Now the improved quality of observations and data input for wave modelling made it impossible to ignore the situations where the discrepancy between the KE based models and observations could not be bridged by any means. The following fundamental shortcomings of the modelling based upon the existing kinetic equation became apparent: (i) By construction, the KE cannot describe reaction of wave fields to rapid perturbations (e.g. abrupt changes of wind, wind gusts, sharp boundaries, etc). (ii) The KE based models can predict evolution of wave spectra only, while it is highly desirable to model the evolution of the wave height probability density function, or, more precisely, its departure from the Gaussian distribution. This, in particular, is badly needed for forecasting rogue waves, but also for assessing the validity of the KE based models. The KE itself 'does not know' when it ceases to be applicable. To address these shortcomings, the following radical ideas have been put forward very recently by the authors. New generalised kinetic equations have been derived from first principles by lifting two most restrictive assumptions: proximity of the wave field to equilibrium, and the oversimplification in taking into account the wave field departure from Gaussianity. Crucially, it was also discovered by the authors that for a typical wind waves it is possible to reconstruct evolution of probability density function once the spectrum is found. The proposal aims at creating a new numerical and conceptual framework for the study of wind wave evolution, by elaborating the above ideas and developing a new way of wind wave modelling based on the novel expression for Snl, derived from first principles. The purpose of this proposal is to create a numerical tool (robust parallel code) for solving the new kinetic equations and then to use this tool to address outstanding questions of wave field evolution. In developing the code, we will be greatly helped by the direct numerical simulation (DNS) algorithm developed by the authors for the simulation of long time evolution of wave field. The algorithm will be used for the validation of the new code. With the help of the new tool, we will delineate the situations where the standard KE is indeed valid and where it ceases to be applicable, and will investigate the regimes of wave evolution well beyond the limits of its applicability (e.g. gusty wind). We will model the evolution of wave field departure from Gaussianity, which, in particular, will make possible to assess probability of freak waves. We will formulate 'practical' parameterisations and recommendations for wave forecasting. This project aims to revolutionise wind wave modelling and forecasting. The new approach we propose is better suited to parallelisation of simulations and increase of power of computers, eventually it will replace the existing algorithms of calculating Snl. It will produce not only a more accurate description of reality, it has the potential to do it faster.