发表机构
Norwegian University of Science and Technology; University of Oslo; Université de Rennes（挪威科技大学; 奥斯陆大学; 雷恩大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究针对固体表面驻点附近的标量混合，提出了解析理论，确定了混合时间尺度，并揭示了浓度衰减和宽度增长的普适标度律。
AI 中文摘要
近期的进展已将多孔介质中的混合与无穷小流体元的变形联系起来。然而，这些拉格朗日框架通常忽略或简化与固体表面的相互作用。我们考虑薄溶质斑块（条带或片状）在单个一般障碍物附近的输运，特别是沿着与固体边界上的驻点相连的分离线（分界线）。在这种情况下，我们证明流动与扩散之间的耦合在解析上是可处理的。我们提供了上游驻点附近标量混合的完整理论，并通过数值模拟进行了验证。我们确定了一个混合时间尺度 $t_B \sim Pe^{1/3}$，其中 $Pe$ 是佩克莱数，它控制标量衰减是由流体拉伸驱动还是由与固体边界的相互作用驱动。渐近地，对于时间 $t < t_B$，我们发现最大浓度 $c_{\rm max}$ 按 $t^{-5/2}$ 衰减，宽度 $\sigma$ 按 $t^{1/2}$ 增长。对于 $t > t_B$，我们发现 $c_{\rm max}$ 呈指数衰减，宽度 $\sigma \sim s_B \sim Pe^{-1/3}$ 为常数，其中 $s_B$ 是一个混合长度尺度，不同于剪切流中出现的尺度。$c_{\rm max}(t)$ 和 $\sigma(t)$ 的渐近标度及其对 $Pe$ 的依赖，对于无滑移驻点是普适的，并且与开放流中的驻点有本质区别。
英文摘要
Recent advances have linked mixing in porous media to the deformation of infinitesimal fluid elements. However, these Lagrangian frameworks generally neglect or simplify interactions with solid surfaces. We consider transport of thin solute blobs (strips or sheets) near single generic obstacles, in particular along separation lines (separatrices) which connect to stagnation points at solid boundaries. In this case, we demonstrate that the coupling between flow and diffusion is analytically tractable. We provide a complete theory for scalar mixing near upstream stagnation points, which we validate by numerical simulations. We identify a mixing time scale $t_B \sim Pe^{1/3}$, where $Pe$ is the Péclet number, which controls whether scalar decay is driven by fluid stretching or by interaction with the solid boundary. Asymptotically, for times $t < t_B$, we find that the maximum concentration $c_{\rm max}$ decays as $t^{-5/2}$ and that the width $σ$ grows like $t^{1/2}$. For $t > t_B$, we find exponential decay of $c_{\rm max}$ and constant width $σ\sim s_B \sim Pe^{-1/3}$, where $s_B$ is a mixing length scale distinct from that which appears in shear flows. The asymptotic scalings of $c_{\rm max}(t)$ and $σ(t)$, and their dependence on $Pe$, are universal to no-slip stagnation points and qualitatively different from stagnation points in open flows.
Comments36 pages, 11 figures
