Title: Turbulence-induced anti-Stokes flow: experiments and theory Show Chinese title

Title: 湍流引起的反斯托克斯流：实验和理论

Abstract: We report experimental evidence of an Eulerian-mean flow, $\overline{u}(z)$, created by the interaction of surface waves and tailored ambient sub-surface turbulence, which partly cancels the Stokes drift, $u_s(z)$, and present supporting theory. Water-side turbulent velocity fields and Eulerian-mean flows were measured with particle image velocimetry before vs after the passage of a wave group, and with vs without the presence of regular waves. We compare different wavelengths, steepnesses and turbulent intensities. In all cases, a significant change in the Eulerian-mean current is observed, strongly focused near the surface, where it opposes the Stokes drift. The observations support the picture that when waves encounter ambient sub-surface turbulence, the flow undergoes a transition during which Eulerian-mean momentum is redistributed vertically (without changing the depth-integrated mass transport) until a new equilibrium state is reached, wherein the near-surface ratio between $\mathrm{d}\overline{u}/\mathrm{d}z$ and $|\mathrm{d}u_s/\mathrm{d} z|$ approximately equals the ratio between the streamwise and vertical Reynolds normal stresses. This accords with a simple statistical theory derived here and holds regardless of the absolute turbulence level, whereas stronger turbulence means faster growth of the Eulerian-mean current. We present a model based on Rapid Distortion Theory which describes the generation of the Eulerian-mean flow as a consequence of the action of the Stokes drift on the background turbulence. Predictions are in qualitative, and reasonable quantitative, agreement with experiments on wave groups, where equilibrium has not yet been reached. Our results could have substantial consequences for predicting the transport of water-borne material in the oceans. Show Chinese abstract

Abstract: 我们报告了实验证据，表明由表面波与定制的次表层湍流相互作用产生的欧拉平均流$\overline{u}(z)$，部分抵消了斯托克斯漂流$u_s(z)$，并提出了支持这一理论的证据。 通过粒子图像测速技术测量了水侧湍流速度场和欧拉平均流，在波群通过前/后以及存在/不存在规则波的情况下进行了测量。 我们比较了不同的波长、陡度和湍流强度。 在所有情况下，观察到了显著的欧拉平均流变化，这种变化主要集中在近表面区域，且与斯托克斯漂流方向相反。 观测结果支持这样一种观点：当波遇到次表层湍流时，流经历了一个过渡阶段，在此期间欧拉平均动量在垂直方向上重新分布（而不改变深度积分的质量传输），直到达到一个新的平衡状态，在这个状态下，近表面区域$\mathrm{d}\overline{u}/\mathrm{d}z$和$|\mathrm{d}u_s/\mathrm{d} z|$的比例大致等于沿流向和垂直方向雷诺正应力的比例。 这与这里推导出的一个简单统计理论一致，并且无论绝对湍流水平如何都成立，而更强的湍流意味着欧拉平均流增长更快。 我们提出了一种基于快速扭曲理论的模型，该模型描述了斯托克斯漂流对背景湍流的作用导致欧拉平均流的产生。 预测结果在波群的实验中，在尚未达到平衡的情况下，在定性及合理的定量上与实验结果一致。 我们的结果可能对预测海洋中水生物质的运输具有重要意义。