  We study the effect of advection on the aggregation and pattern formation in
chemotactic systems described by Keller-Segel type models. The evolution of
small perturbations is studied analytically in the linear regime complemented
by numerical simulations. We show that a uniform differential flow can
significantly alter the spatial structure and dynamics of the chemotactic
system. The flow leads to the formation of anisotropic aggregates that move
following the direction of the flow, even when the chemotactic organisms are
not directly advected by the flow. Sufficiently strong advection can stop the
aggregation and coarsening process that is then restricted to the direction
perpendicular to the flow.
