Abstract This study is concerned with the characteristics of coherent vortices within the turbulent air flow undulated by gravity and capillary–gravity water waves. The flow fields from the direct numerical simulations are analyzed. A formal scheme is developed to detect and classify the vortical structures. The scheme uses local analysis of the velocity-gradient tensor to define the vortex swirling core, and adopts the topological geometry of the swirling core to classify the vortical structures. Three types of vortical structures are identified, including quasi-streamwise vortex, reversed and forward (head pointing upstream and downstream, respectively) horseshoe vortices. Quasi-streamwise vortices are the dominant structure in the flow; their distribution initiates near the wave trough, extends downstream along the windward face, lifts up and terminates above the wave crest. More reversed horseshoe vortices are observed than the forward horseshoe vortices; both cluster around the region above wave trough. Reversed and forward horseshoe vortices, however, contribute the most to the production of Reynolds stress associated with sweep and ejection motions, respectively. The quasi-streamwise vortices contribute more to producing Reynolds stress associated with ejection event, indicating that the elongated vortices bend inward at the downstream end and can be considered as degenerate forward horseshoe vortices. The intensified distributions of horseshoe vortices near the wave trough are attributed to the combined effect of vortex turning from the spanwise turbulent component to the streamwise vortex and the vortex stretching of the streamwise vortex. The strong stretching of streamwise vortex above the windward face contributes to the continuous development of quasi-streamwise vortices. Accordingly, the presence of capillary ripples on the windward face mitigates effectively the occurrence of coherent vortices, in particular the quasi-streamwise vortices. In contrast, the presence of capillary ripples on the leeward surface presents a minor effect on the mitigation of coherent vortices.

中文翻译：

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毛细管重力水面波上湍流气流的研究：相干涡旋结构的特征

摘要 本研究关注由重力和毛细重力水波波动的湍流气流中的相干涡流特征。分析来自直接数值模拟的流场。开发了一种正式的方案来检测和分类涡旋结构。该方案利用速度梯度张量的局部分析来定义涡旋涡旋核，并采用涡旋核的拓扑几何对涡旋结构进行分类。确定了三种类型的涡旋结构，包括准流向涡旋、反向和向前（头部分别指向上游和下游）马蹄形涡旋。准流向涡是流动中的主要结构；它们的分布始于波谷附近，沿迎风面向下游延伸，升起并终止于波峰上方。与正向马蹄形涡旋相比，观察到更多的反向马蹄形涡旋；两者都聚集在波谷上方的区域周围。然而，反向和向前马蹄形涡旋对分别与扫掠和弹射运动相关的雷诺应力的产生贡献最大。准流向涡对产生与喷射事件相关的雷诺应力的贡献更大，表明细长涡在下游端向内弯曲，可以认为是退化的前向马蹄涡。波谷附近马蹄形涡的强化分布是涡从展向湍流分量转向流向涡和流向涡的涡拉伸的综合作用。迎风面上方流向涡的强烈拉伸有助于准流向涡的不断发展。因此，迎风面上毛细波纹的存在有效地减轻了相干涡流的发生，特别是准流向涡流。相比之下，背风面上毛细波纹的存在对减少相干涡流的影响很小。