Modeling Steep Surface Waves Evolving Under Wind Forcing and Energy Dissipation Due to Wave Breaking

海浪在许多科学和工程领域发挥着重要作用，特别是气候学、气象学、海洋环境、海洋运输和海岸工程。它们是通过从风中汲取能量产生的，通过非线性波浪相互作用而演变，最终通过波浪破碎而消散。当完全发展时，海浪的波长从厘米(毛细管波)到千米(海啸)。在如此广泛的空间尺度上计算求解海浪模型是一个巨大的挑战，而且在大面积海洋上求解完整的水动力学方程是不切实际的。这些事实引起了人们对开发一种新颖而有效的计算工具的日益浓厚的兴趣，该工具可以同时处理风强迫、破碎波消散和非线性波相互作用。本研究项目旨在为这一工具的开发做出贡献。一旦开发出来，计算模型将对从事物理海洋过程和气候变化工作的研究人员有用，因为跨越海-气边界的能量和动量转移是他们工作的基础。为了准确地预测非线性表面波的演化，这位研究人员和他的同事们结合波浪破碎和风浪相互作用的理论模型，开发了一个可靠而有效的相分辨波浪模型。通过伪谱方法的数值模拟和室内对比试验，检验了积分海浪模式对风压作用下陡峭海面波的预报能力。为了实现这一目标，首先通过对波浪模型的数值模拟确定一个稳健的破裂准则，然后用实验室实验进行验证。然后，通过对陡波变形面的粘性边界层分析，根据局部流动和波动特性，确定了粘性能量耗散率和自由面上的气压分布，以及气流分离的判据。通过将边界层分析的结果与波浪破碎和风浪相互作用试验的测量相结合，确定了能量耗散项和风强迫项，并将其整合到波浪预报模式中。最后，通过数值解与实验结果的比较，验证了所建立的波浪模型的正确性。

Ocean waves play an important role in many areas of science and engineering, notably climatology, meteorology, ocean environment, marine transport, and coastal engineering. They are generated by drawing energy from wind, evolve through nonlinear wave interactions, and are eventually dissipated by wave breaking. When fully developed, ocean waves have wavelengths that span scales from centimeters (capillary waves) to kilometers (tsunami). Computationally resolving models for ocean waves over such a wide range of spatial scales is an enormous challenge, and it is impractical to solve the full hydrodynamic equations over a large surface area of the ocean. These facts have produced an increasing interest in developing a novel and efficient computational tool that can simultaneously treat wind forcing, breaking wave dissipation, and nonlinear wave interactions. This research project aims to contribute to the development of such a tool. Once it is developed, the computational model would be useful for researchers working on physical oceanographic processes and climate change, because the transfer of energy and momentum across the air-sea boundary is fundamental to their work. A graduate student is involved in the project.To predict accurately the evolution of nonlinear surface waves, the investigator and his colleagues develop a reliable and efficient phase-resolving wave model combined with theoretical models of wave breaking and wind-wave interaction. Through numerical simulations using a pseudo-spectral method and controlled laboratory experiments, the predictive capability of the integrated wave model is examined for steep surface waves evolving under wind forcing. To achieve this goal, a robust breaking criterion is first determined though numerical simulations of the wave model and then is confirmed with laboratory experiments. Then, through viscous boundary layer analyses at the deformed surface of steep waves, the viscous energy dissipation rate and the air pressure distribution over the free surface, as well as a criterion of airflow separation, is identified in terms of local flow and wave characteristics. By coupling the results of the boundary layer analyses with measurements of wave breaking and wind-wave interaction experiments, the energy dissipation and wind forcing terms are determined and integrated into the wave prediction model. Finally, the resulting wave model is validated by comparing its numerical solutions with laboratory experiments.