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arXiv 2307.12367physics.flu-dyn
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风浪在粘性液体上的增长

Wind-wave growth over a viscous liquid

J. Zhang, A. Hector, M. Rabaud, F. Moisy

AI总结:

本研究通过实验和理论分析,探讨了液体粘度对风浪增长的影响,验证了Miles模型在粘性液体中的适用性,并揭示了增长率及临界摩擦速度随粘度的标度关系。

摘要:

关于风浪生成的实验和理论研究主要集中于空气-水界面,在该界面处粘性效应较小。本文研究了液体粘度对机械生成波浪增长的影响。在我们的实验中,风吹过一层硅油,其粘度为水的20倍和50倍,通过浸入式造波机激发小振幅波浪。我们使用基于折射的光学方法——自由表面合成纹影法,测量了波浪斜率包络的空间演变。通过对表面斜率进行时空带通滤波,我们能够选择性地确定每个强迫频率下的空间增长率,即使强迫波被阻尼并且与其他频率下自然放大的波共存。我们系统地测量了不同风速和波频率下的增长率,从而能够精确确定边际稳定性曲线和波浪增长的起始点。我们表明,通常应用于水波的Miles模型能够为粘性更大的液体提供合理的增长率描述。最后,我们讨论了最大放大波的增长率以及临界摩擦速度随液体粘度的标度关系。

英文摘要:

Experimental and theoretical studies on wind-wave generation have focused primarily on the air-water interface, where viscous effects are small. Here we characterize the influence of the liquid viscosity on the growth of mechanically generated waves. In our experiment, wind is blowing over a layer of silicon oil, of viscosity 20 and 50 times that of water, and waves of small amplitude are excited by an immersed wave-maker. We measure the spatial evolution of the wave slope envelope using Free-Surface Synthetic Schlieren, a refraction-based optical method. Through spatiotemporal band-pass filtering of the surface slope, we selectively determine the spatial growth rate for each forcing frequency, even when the forced wave is damped and coexists with naturally amplified waves at other frequencies. Systematic measurements of the growth rate for various wind velocities and wave frequencies are obtained, enabling precise determination of the marginal stability curve and the onset of wave growth. We show that Miles' model, which is commonly applied to water waves, offers a reasonable description of the growth rate for more viscous liquids. We finally discuss the scaling of the growth rate of the most amplified wave and the critical friction velocity with the liquid viscosity.

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