自由表面曲率及其与亚表面湍流的关系
Free-surface curvature and its relation to subsurface turbulence
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中文总结 AI 辅助
本文开发理论框架模拟自由表面变形，经实验验证表面曲率与近表面速度场曲率高度相关，可通过表面变形感知亚表面流动状态，为光学推断近表面湍流过程提供基础。
中文摘要 AI 辅助
湍流液体流动顶部的自由表面会被下方流体运动变形，湍流将其几何特征印记在表面上。本文基于含重力和表面张力的欧拉方程，开发了一个理论框架来模拟此类变形，并通过零平均流湍流水箱中表面形貌与亚表面速度场的同步高分辨率测量对其进行评估。研究考虑了一系列雷诺数和弗劳德数，重点关注表面未破裂的工况。在一系列空间和时间尺度上，从统计以及局部/瞬时角度来看，测得的表面曲率与基于表面下方几毫米处速度场建模得到的曲率之间存在密切的定量一致性。重要的是，我们验证了表面曲率的大小与近表面水平速度的散度之间存在强相关性，而该散度又直接与气-水界面的气体和热传递相关。我们讨论了随深度增加的亚表面运动如何与表面形状去相关，且在更小的空间尺度上这种去相关发生得更快。这些发现表明，表面变形的测量可用于感知表面下方的流动状态，并为基于光学推断近表面湍流控制的过程奠定了基础。
英文摘要
The free surface atop a turbulent liquid flow is deformed by the underlying fluid motion, with the turbulence imprinting its geometry on the surface. Here we develop a theoretical framework to model such deformations based on the Euler equation with gravity and surface tension, and evaluate it against simultaneous high-resolution measurements of surface topography and subsurface velocity fields in a zero-mean-flow turbulent water tank. We consider a range of Reynolds and Froude numbers, focusing on regimes in which the surface is unbroken. Over a range of spatial and temporal scales, we find close quantitative agreement between the measured surface curvature and that which is modeled based on the velocity field a few millimeters beneath the surface, both from the statistical and the local/instantaneous standpoints. Importantly, we verify a strong correlation between the magnitudes of the surface curvature and the divergence of the near-surface horizontal velocity, which in turn is directly related to gas and heat transfer at the air-water interface. We discuss how the sub-surface motion at increasing depths decorrelates from the surface shape, and does so more rapidly at smaller spatial scales. These findings demonstrate that measurements of surface deformations may be used to sense the state of the flow beneath the surface and provide a foundation to make optically-based inferences of processes controlled by near-surface turbulence.
