湍流自由表面流中凹坑与划痕下方的涡结构
Vortex structures under dimples and scars in turbulent free-surface flows
AI总结：
本研究通过直接数值模拟探究湍流自由表面的凹坑、划痕痕迹与下方涡结构的关联，明确了两类痕迹下涡存在概率的深度分布规律与涡取向特征，提出划痕是表层下约1/4泰勒微尺度处水平涡的印记。
摘要：
自由表面下方的湍流会在表面留下特征性的长寿命痕迹，例如上涌的“泡状流（boils）”、近圆形的“凹坑（dimples）”和细长的“划痕（scars）”，这些痕迹肉眼很容易识别，比如在河流流动中。本文中，我们使用直接数值模拟（Direct Numerical Simulations）来探究这些表面痕迹与下方涡结构之间的联系。我们通过分析痕迹下方某点位于涡核内的条件概率，以及痕迹下方涡量的倾角，研究了已知为表面附着涡印记的凹坑，以及尚未得到广泛研究的划痕。分析表明，凹坑下方存在涡的概率从表面向下穿过黏性层和阻塞层时以近似高斯的方式下降，这一过程受凹坑尺寸和整体湍流的影响。当以泰勒微尺度$λ_T$归一化的深度为函数表示时，该概率与雷诺数和韦伯数无关。相反，划痕下方存在涡的概率从表面开始急剧上升，在黏性层边缘、深度约为$λ_T/4$处达到峰值。涡取向的分布也呈现出清晰的模式：凹坑下方的涡强烈倾向于垂直排列，而划痕下方的涡同样强烈地倾向于水平排列。我们的研究结果表明，划痕可以被定义为表面下方约四分之一泰勒微尺度深度处的水平涡的印记，这类似于凹坑可被定义为表面附着的垂直涡管的印记。
英文摘要：
Turbulence beneath a free surface leaves characteristic long-lived signatures on the surface, such as upwelling 'boils', near-circular 'dimples' and elongated 'scars', easily identifiable by eye, e.g., in riverine flows. In this paper, we use Direct Numerical Simulations to explore the connection between these surface signatures and the underlying vortical structures. We investigate dimples, known to be imprints of surface-attached vortices, and scars, which have yet to be extensively studied, by analysing the conditional probabilities that a point beneath a signature is within a vortex core as well as the inclination angles of sub-signature vorticity. The analysis shows that the likelihood of vortex presence beneath a dimple decreases from the surface down through the viscous and blockage layers in a near-Gaussian manner, influenced by the dimple's size and the bulk turbulence. When expressed as a function of depth over the Taylor microscale $λ_T$, this probability is independent of Reynolds and Weber number. Conversely, the probability of finding a vortex beneath a scar increases sharply from the surface to a peak at the edge of the viscous layer, at a depth of approximately $λ_T/4$. Distributions of vortical orientation also show a clear pattern: a strong preference for vertical alignment below dimples and an equally strong preference for horizontal alignment below scars. Our findings suggest that scars can be defined as imprints of horizontal vortices approximately a quarter of the Taylor microscale beneath the surface, analogous to how dimples can be defined as imprints of surface-attached vertical vortex tubes.
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