Christov Ivan C, Ottino Julio M, Lueptow Richard M
Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, Illinois 60208, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2010 Apr;81(4 Pt 2):046307. doi: 10.1103/PhysRevE.81.046307. Epub 2010 Apr 12.
We study a singular limit of tumbled granular flows in quasi-two-dimensional rotating drums, demonstrating that the limiting dynamical system, as the shear layer vanishes, belongs to a class of discrete discontinuous mappings called piecewise isometries. In doing so, we identify a mechanism of mixing, in the absence of the usual streamline crossing mediated by the flowing layer. By considering the exceptional case of a 50% full square tumbler, this mechanism (streamline jumping) is related to the horizontal motion of the free surface of the flow in non-half-full tumblers. The limiting dynamics are quite complex, if not (technically) chaotic.
我们研究了准二维旋转鼓中翻滚颗粒流的奇异极限，证明了随着剪切层消失，极限动力系统属于一类称为分段等距映射的离散不连续映射。在此过程中，我们确定了一种混合机制，这种机制不存在由流动层介导的通常的流线交叉现象。通过考虑半满方形容器这一特殊情况，这种机制（流线跳跃）与非半满容器中流体自由表面的水平运动有关。极限动力学相当复杂，即便（从技术角度讲）不是混沌的。
