  We demonstrate a novel shear-induced mechanism for growth of concentration
fluctuations in a bacterial suspension. Using a linear stability analysis, a
homogeneously sheared suspension is shown to support exponentially growing
layering perturbations in the shear-rate and bacterial concentration.
Non-linear simulations show that the instability eventually leads to
gradient-banded velocity profiles, with a local depletion of bacteria at the
interface between the bands. Our results show that long-ranged hydrodynamic
interactions are sufficient to explain recent observations of shear-bands in
bacterial suspensions.
