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风生浪各阶段特征演化数值模拟

SIMULATION OF WIND-DRIVEN WAVE CHARACTERISTIC EVOLUTION AT DIFFERENT STAGES

  • 摘要: 风波增长现象广泛存在于自然中. 尽管通过实验研究已经提出了多种理论假设, 但由于风场和波场的随机性和多尺度特性, 未能通过实验获得可靠的原理解释其机理. 随着计算流体力学的发展, 对风波演化进行数值模拟以研究其生成机理更为便利. 文章基于自主开发的直角网格两相流求解器, 结合高阶数值格式和VOF (volume of fluid)界面捕捉方法, 对 1.6\;\mathrmm/\mathrms的风驱动自由液面进行数值模拟, 获得的波浪增长过程由线性增长阶段和指数增长阶段组成. 为分析能量特征, 计算了能量集中的主要波数, 并结合波高、波斜率与波数的变化与实验相对比. 在一维波数空间中统计能量分布, 与Kolmogorov-Zakharov E\left(k\right)\sim k^-15/4 幂律进行对比. 在二维波数和时域空间中, 增长前期应用Phillips线性增长理论和共振加强后的增长模型对风波线性增长阶段进行验证; 增长后期应用Miles理论对风波指数增长进行验证. 揭示了风波增长不同阶段的机理特征, 观察到在指数增长开始前, 波浪的线性增长存在初始响应阶段、风压稳定阶段和风压受扰阶段, 分别具有不同的机理特征. 证明了波浪演化的初始线性阶段是由湍流波动产生的随机尾流叠加占主导, 而后期的指数增长阶段是由增长率和摩擦速度正相关占主导. 原始的Phillips理论仅在增长初始响应阶段准确, 使用共振加强修正后则在初始响应后也符合实际增长, 而Miles理论仅在单色波阶段时才准确. 相较于对波陡有限制的动态曲线网格求解器, 应用5阶WENO (weighted essentially non-oscillation)和动量−质量一致推进方法修正的VOF方法也可用于分析风波增长问题的求解, 并能准确捕捉到更多风波增长的细节.

     

    Abstract: Wind and wave growth is widespread in nature and industry. Due to the randomness and multi-scale characteristics of wind field and wave field, no reliable principles can be obtained through experiments to explain the mechanism. It is very necessary to study the generation mechanism of wind and wave evolution through detailed simulation. In this paper, a wind-driven free surface with a wind speed of 1.6 m/s is numerically simulated. The wave growth obtained consists of linear and exponential growth phases defined by the earlier theory. According to the wind and wave characteristics, as well as the two-dimensional wave number and the energy distribution in the frequency domain space, the mechanism characteristics of wind and wave growth in different stages are revealed. The mechanism characteristics of waves in different stages are revealed. It is observed that before exponential growth, the linear growth of waves has initial response stage, wind pressure stable stage and wind pressure disturbed stage, which have different mechanism characteristics respectively. The original Phillips theory is accurate only in the initial response phase of growth, and resonance enhanced theory is also consistent with the actual growth after the initial response. while the Miles theory is accurate only in the monochromatic wave phase.

     

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