  We consider the effect of radial fluid injection and suction on
Taylor-Couette flow. Injection at the outer cylinder and suction at the inner
cylinder generally results in a linearly unstable steady spiralling flow, even
for cylindrical shears that are linearly stable in the absence of a radial
flux. We study nonlinear aspects of the unstable motions with the energy
stability method. Our results, though specialized, may have implications for
drag reduction by suction, accretion in astrophysical disks, and perhaps even
in the flow in the earth's polar vortex.
