  We study a collection of polar self-propelled particles confined to a long
two-dimensional channel. We write the coupled hydrodynamic equations of motion
for density and polarisation order parameter. At two confined boundaries,
density is fixed to the mean and orientation is anti-parallel with fixed
magnitude of polarisation. Such boundary conditions make our system similar to
a sheared suspension of self-propelled particles, which has many practical
applications. Antiparallel alignment at the two confined boundaries and
alignment inside the channel create rolls of orientation along the long axis of
the channel. For zero self-propulsion speed, density and orientation fields are
decoupled and density remains homogeneous inside the channel. For finite
self-propelled speed, density inhomogeneities develop and these rolls move
along the long axis of the channel. Density inhomogeneity increases sharply
with increasing the self propulsion speed and then reaches a maximum and again
decreases for very large speeds. Formation of rolls is very similar to the
classic problem of Rayleigh-Benard convection in fluid dynamics.
