标题： 风浪的数值模拟。 问题、解决方案、验证和应用 显示英文标题

标题： Numerical Modelling of Wind Waves. Problems, Solutions, Verifications, and Applications

摘要： 场的时间-空间演化由二维波能谱密度S(x,t)的输运方程描述，该方程在空间x和时间t中展开。该方程具有一个称为源函数的强迫项F，F依赖于波谱S以及外部造波因素：局部风W(x, t)和局部流U(x, t)。源函数包含负责波谱演化的某些物理机制。它用于区分函数F中的三个项：风-波能量交换机制In；非线性波-波相互作用的能量守恒机制Nl；以及波能量损失机制Dis。源函数项的数学表示差异决定了波浪模型之间的总体差异。问题是根据基本波浪方程推导出上述源函数项的解析表达式。基于众多作者的出版物以及作者过去二十年的研究，已经构建了源函数F的所有主要项的优化版本。详细描述了这些结果。源函数的最终版本在学术测试任务中进行了测试，并通过将其纳入著名的风浪模型WAM和WAVEWATCH的数值壳层进行了验证。测试和验证程序被详细地呈现和描述。展示了所提出的新的源函数在计算精度和速度方面的优越性。最后，提出了该领域未来发展的方向，并展示了一些数值风浪模型可能的应用，旨在研究风浪物理和气候尺度上的全球风浪变化，包括风、波浪和上层水体之间的机械能交换。 显示英文摘要

摘要： The time-space evolution of the field is described by the transport equation for the 2-dimensional wave energy spectrum density, S(x,t), spread in the space, x, and time, t. This equation has the forcing named the source function, F, depending on both the wave spectrum, S, and the external wave-making factors: local wind, W(x, t), and local current, U(x, t). The source function contains certain physical mechanisms responsible for a wave spectrum evolution. It is used to distinguish three terms in function F: the wind-wave energy exchange mechanism, In; the energy conservative mechanism of nonlinear wave-wave interactions, Nl; and the wave energy loss mechanism, Dis. Differences in mathematical representation of the source function terms determine general differences between wave models. The problem is to derive analytical representations for the source function terms said above from the fundamental wave equations. Basing on publications of numerous authors and on the last two decades studies of the author, the optimized versions of the all principal terms for the source function, F, have been constructed. Detailed description of these results is presented. The final version of the source function is tested in academic test tasks and verified by implementing it into numerical shells of the well known wind wave models: WAM and WAVEWATCH. Procedures of testing and verification are presented and described in details. The superiority of the proposed new source function in accuracy and speed of calculations is shown. Finally, the directions of future developments in this topic are proposed, and some possible applications of numerical wind wave models are shown, aimed to study both the wind wave physics and global wind-wave variability at the climate scale, including mechanical energy exchange between wind, waves, and upper water layer.