Solomon T H, Mezić Igor
Department of Physics, Bucknell University, Lewisburg, Pennsylvania 17837, USA.
Nature. 2003 Sep 25;425(6956):376-80. doi: 10.1038/nature01993.
Laminar flows can produce particle trajectories that are chaotic, with nearby tracers separating exponentially in time. For time-periodic, two-dimensional flows and steady three-dimensional (3D) flows, enhancements in mixing due to chaotic advection are typically limited by impenetrable transport barriers that form at the boundaries between ordered and chaotic mixing regions. However, for time-dependent 3D flows, it has been proposed theoretically that completely uniform mixing is possible through a resonant mechanism called singularity-induced diffusion; this is thought to be the case even if the time-dependent and 3D perturbations are infinitesimally small. It is important to establish the conditions for which uniform mixing is possible and whether or not those conditions are met in flows that typically occur in nature. Here we report experimental and numerical studies of mixing in a laminar vortex flow that is weakly 3D and weakly time-periodic. The system is an oscillating horizontal vortex chain (produced by a magnetohydrodynamic technique) with a weak vertical secondary flow that is forced spontaneously by Ekman pumping--a mechanism common in vortical flows with rigid boundaries, occurring in many geophysical, industrial and biophysical flows. We observe completely uniform mixing, as predicted by singularity-induced diffusion, but only for oscillation periods close to typical circulation times.
层流可以产生混沌的粒子轨迹，附近的示踪剂会随时间呈指数分离。对于时间周期的二维流和稳定的三维（3D）流，由混沌平流引起的混合增强通常受到在有序和混沌混合区域之间的边界处形成的不可穿透的输运屏障的限制。然而，对于随时间变化的3D流，从理论上提出通过一种称为奇点诱导扩散的共振机制可以实现完全均匀的混合；即使随时间变化的和3D扰动无限小，人们也认为情况就是如此。确定实现均匀混合的条件以及这些条件在自然界中通常出现的流中是否得到满足是很重要的。在这里，我们报告了对一种弱三维和弱时间周期的层流涡旋流中混合的实验和数值研究。该系统是一个振荡的水平涡旋链（由磁流体动力学技术产生），具有一个弱的垂直二次流，该二次流由埃克曼抽吸自发驱动——这是一种在具有刚性边界的涡旋流中常见的机制，发生在许多地球物理、工业和生物物理流中。正如奇点诱导扩散所预测的那样，我们观察到了完全均匀的混合，但仅在振荡周期接近典型循环时间时才会出现。
