论文标题
表征由流体流动驱动的有效扩散的比例依赖性
Characterizing scale dependence of effective diffusion driven by fluid flows
论文作者
论文摘要
我们研究流体示踪剂有效扩散的量表依赖性，特别是其对péclet数量的依赖性，这是对流与分子扩散之间比率的无量纲参数。在这里，我们解决了可以描述有效扩散的长度和时间尺度与对流和分子扩散的情况。为此，我们提出了一种在不依赖于尺度分离的情况下表征有效扩散率的新方法。对于可以出现有效扩散的给定空间结构域，通过考虑测试对流扩散方程的时空演化来识别与扩散相关的时间常数，其中其初始条件在脉冲函数上设置为脉冲函数。然后，通过最小化上述测试方程解决方案之间的$ l_ \ infty $距离来识别有效扩散率的值，并具有平均漂移的扩散。对于这种方法，对于时间独立的Gyre和时间周期性剪切流，我们从数值上显示了有效扩散率的规模依赖性及其与规模分离假设的经典限制的差异。差异的运动起源被揭示为分子扩散跨回旋的流动细胞的发展，以及由于剪切中的时间振荡而导致的漂移运动的抑制。
We study the scale dependence of effective diffusion of fluid tracers, specifically, its dependence on the Péclet number, a dimensionless parameter of the ratio between advection and molecular diffusion. Here, we address the case that length and time scales on which the effective diffusion can be described are not separated from those of advection and molecular diffusion. For this, we propose a new method for characterizing the effective diffusivity without relying on the scale separation. For a given spatial domain inside which the effective diffusion can emerge, a time constant related to the diffusion is identified by considering the spatio-temporal evolution of a test advection-diffusion equation, where its initial condition is set at a pulse function. Then, the value of effective diffusivity is identified by minimizing the $L_\infty$ distance between solutions of the above test equation and the diffusion one with mean drift. With this method, for time-independent gyre and time-periodic shear flows, we numerically show the scale dependence of the effective diffusivity and its discrepancy from the classical limits that were derived on the assumption of the scale separation. The kinematic origins of the discrepancy are revealed as the development of the molecular diffusion across flow cells of the gyre and as the suppression of the drift motion due to a temporal oscillation in the shear.
