Elastoinertial chains in a two-dimensional turbulent flow

The interplay of inertia and elasticity is shown to have a significant impact on the transport of filamentary objects, modeled by bead-spring chains, in a two-dimensional turbulent flow. We show how elastic interactions among inertial beads result in a nontrivial sampling of the flow, ranging from entrapment within vortices to preferential sampling of straining regions. This behavior is quantified as a function of inertia and elasticity and is shown to be very different from free, noninteracting heavy particles, as well as inertialess chains [Picardo et al., Phys. Rev. Lett. 121, 244501 (2018)]. In addition, by considering two limiting cases, of a heavy-headed and a uniformly inertial chain, we illustrate the critical role played by the mass distribution of such extended objects in their turbulent transport.

Figure 1

A schematic of (a) a uniformly inertial and (b) a heavy-headed chain illustrating the notation used in the text.

Figure 2

Representative snapshots of a randomly chosen subset of (a) noninteracting inertial particles, as well as (b) heavy-headed chains and (c) uniformly inertial chains overlaid on the vorticity field. The centers of mass of the chains are shown by red dots [like the free particles in panel (a)] and the chain itself by black lines. The inset in panel (b) shows a zoomed-in view of the vortex located near the top-left corner of this panel. We show results for $\mathrm{St}=0.14$ and $\mathrm{Wi}=1.38$ [for panels (b) and (c)].

Figure 3

PDFs of ${\mathrm{\Lambda }}_c$ measured for uniformly inertial chains with (a) $\mathrm{St}=0.14$, (b) $\mathrm{St}=0.85$, and (c) $\mathrm{St}=2.84$. Curves are plotted for different degrees of elasticity of the chains, as well as for noninteracting inertial particles (see legend). The insets show the same distributions for the heavy-headed chains, but for only two values of $\mathrm{Wi}$.

Figure 4

(a) Pseudocolor plots of the skewness $\gamma$ of the distribution of ${\mathrm{\Lambda }}_c$, in the $\mathrm{St}\text{−}\mathrm{Wi}$ plane, for uniformly inertial chains. For comparison, the same skewness obtained for noninteracting particles is shown in panel (b). We also show in panel (c) the average normalized length of the inertial chains as a function of $\mathrm{St}$ for a few representative values of $\mathrm{Wi}$.

Figure 5

PDF of the interbead separation $r$ for uniformly inertial ($\mathrm{St}=0.14$) chains, for different values of $\mathrm{Wi}$ (see legend). The solid (black) vertical line corresponds to the maximum link length $r_m$ and the dashed-dot (magenta) line corresponds to $r_0$ which sets the equilibrium link length. With increasing elasticity, we see the distributions develop broader tails and eventually, at large values of $\mathrm{Wi}$, peak near $r_m$.