Figure 1

(a) For $\eta =4000$ and $\alpha =1/\pi$, the center-of-mass trajectory of a meandering filament (box is $100\times 120$ cells). The inset shows the streamlines (light dashed curves) of four quarter-cells of the periodic background flow, with (elliptic) vortical centers at each corner, and a hyperbolic stagnation point at the center. Also shown is a filament undergoing a stretch-coil instability as its transits through the center stagnation point (entering right, exiting down). The thick dashed curves separate regions of transport from entrapment, the dynamics of the latter shown by the filament shapes within. (b) The histogram of fiber elastic energy $2\mathcal{E}$. The inset shows a sample evolution of $2\mathcal{E}$.Reuse & Permissions

Figure 2

Growth rate for the two dominant bending modes versus $\eta$ for a filament aligned with the stable manifold ($\theta =0$). The “E” and “O” label whether the dominant eigenfunction is even or odd about the filament center. The onset of buckling instabilities occurs for an even mode at ${\eta }_c\approx 328$. The inset shows the regions of compressive flow (potentially yielding a buckling instability) and extensional flow around the hyperbolic stagnation point for the straining flow $\mathbf{U}=(-x,y,0)$.Reuse & Permissions

Figure 3

Residence time frequency for $\eta =4000$ and $\alpha =1/\pi$. The dashed line is $P(\tau )$ with $\Delta \tau =6.5$. The vertical lines correspond to the frequency peaks. The inset shows an idealized filament trajectory across the network of hyperbolic points.Reuse & Permissions

Figure 4

Filament dispersion versus time for $\alpha =1/\pi$ and various $\eta$, each estimated by an ensemble average of 80 simulations. The dashed line is the estimate for a random walker, $d^2(t)=4Dt$, using the estimated diffusion $D=0.38$ for $\eta =4000$ (cf. curve 2).Reuse & Permissions

Figure 5

Phase diagram of filament dynamics in cellular flow. For a given $\alpha$, there is a range of $\eta$ for meandering. The dashed line is the stretch-coil instability threshold. Inset at left shows the probability for a filament to be trapped in the cell as a function of initial distance to the manifold for $\alpha =1/\pi$. Inset at right is for $\alpha =1.5/\pi$ and $\eta =80000$. Animations of filament dynamics can be found at 19.Reuse & Permissions

Figure 6

The probability of filament center-of-mass speed.Reuse & Permissions