Emergent scar lines in chaotic advection of passive directors

Abstract

We examine the spatial field of orientations of slender fibers that are advected by a two-dimensional fluid flow. The orientation field of these passive directors are important in a wide range of industrial and geophysical flows. We introduce emergent scar lines as the dominant coherent structures in the orientation field of passive directors in chaotic flows. Previous work has identified the existence of scar lines where the orientation rotates by {\pi} over short distances, but the lines that were identified disappeared as time progressed. As a result, earlier work focused on topological singularities in the orientation field which we find to play a negligible role at long times. We use the standard map as a simple time-periodic two-dimensional (2D) flow that produces Lagrangian chaos. This class of flows produce persistent patterns in passive scalar advection, and we find that a different kind of persistent pattern develops in the passive director orientation field. We identify the mechanism by which emergent scar lines grow to dominate these patterns at long times in complex flows. Emergent scar lines form where the recent stretching of the fluid element is perpendicular to earlier stretching. Thus these scar lines can be labeled by their age, defined as the time since their stretching reached a maximum.