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

海浪在科学和工程的许多领域中发挥着重要作用，特别是气候学，气象学，海洋环境，海洋运输和海岸工程。 它们通过从风中汲取能量而产生，通过非线性波浪相互作用而演变，并最终通过波浪破碎而消散。 当充分发展时，海浪的波长从厘米（毛细波）到公里（海啸）不等。 在如此宽的空间尺度范围内计算求解海浪模型是一个巨大的挑战，并且在海洋的大表面积上求解完整的流体动力学方程是不切实际的。 这些事实产生了越来越多的兴趣，开发一种新的和有效的计算工具，可以同时处理风强迫，破碎波耗散，和非线性波的相互作用。 该研究项目旨在为开发这样一种工具作出贡献。 一旦开发出来，计算模型将对从事物理海洋学过程和气候变化研究的研究人员有用，因为能量和动量跨越海气边界的转移对他们的工作至关重要。 为了准确预测非线性表面波的演变，研究人员和他的同事们开发了一个可靠而有效的相分辨波浪模型，结合了波浪破碎和风浪相互作用的理论模型。 通过使用伪谱方法和受控实验室实验的数值模拟，综合波模型的预测能力进行检查下风强迫陡峭的表面波演变。 为了实现这一目标，一个强大的破碎准则，首先确定通过数值模拟的波浪模型，然后与实验室实验确认。 然后，通过粘性边界层分析在陡峭的波浪变形的表面，粘性能量耗散率和空气压力分布在自由表面上，以及气流分离的标准，根据当地的流动和波浪的特性。 通过将边界层分析的结果与波浪破碎和风浪相互作用实验的测量结果相耦合，确定了能量耗散项和风强迫项，并将其集成到波浪预报模型中。 最后，通过将数值解与实验室试验结果进行比较，验证了所建立的波浪模型的有效性。

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.