  To rotate continuously without jamming, the flagellar filaments of bacteria
need to be locked in phase. While several models have been proposed for
eukaryotic flagella, the synchronization of bacterial flagella is less well
understood. Starting from a reduced model of flexible and
hydrodynamically-coupled bacterial flagella, we rigorously coarse-grain the
equations of motion using the method of multiple scales, and hence show that
bacterial flagella generically synchronize to zero phase difference via an
elastohydrodynamic mechanism. Remarkably, the far-field rate of synchronization
is maximized at an intermediate value of elastic compliance, with surprising
implications for bacteria.
