Pairwise and collective behavior between model swimmers at intermediate Reynolds numbers

Abstract: We computationally studied the pair interactions and collective behavior of asymmetric, dumbbell swimmers over a range of intermediate Reynolds numbers and initial configurations. Depending on the initial positions and the Re, we found that two swimmers either repelled and swum away from one another or assembled one of four stable pairs: in-line and in-tandem, both parallel and anti-parallel. When in these stable pairs, swimmers were coordinated, swum together, and generated fluid flows as one. We compared the stable pairs' speeds, swim direction and fluid flows to those of the single swimmer. The in-line stable pairs behaved much like the single swimmer transitioning from puller-like to pusher-like stroke-averaged flow fields. In contrast, for the in-tandem pairs we discovered differences in the swim direction transition, as well as the stroke-averaged fluid flow directions. Notably, the in-tandem V pair switched its swim direction at a higher $\text{Re}$ than the single swimmer while the in-tandem orbiting pair switched at a lower $\text{Re}$. We also studied a system of 122 swimmers and found the collective behavior transitioned from in-line network-like connections to small, transient in-tandem clusters as the Reynolds number increased, consistent with the in-line to in-tandem pairwise behavior. Details in the collective behavior involved the formation of triples and other many-body hydrodynamic interactions that were not captured by either pair or single swimmer behavior. Our findings demonstrate the richness and complexity of the collective behavior of intermediate-$\text{Re}$ swimmers.