The cylindrical, axisymmetric Navier-Stokes equations are solved numerically to study the generation and evolution of vorticity in an injection-induced transient shear flow. An initially steady internal flowfield driven by constant sidewall injection is disturbed by positive transient sidewall injection, which simulates the unsteady mass input from propellant burning variations. The disturbance amplitude is as large as that of the steady sidewall injection to ensure that nonlinear effects influence the vorticity field evolution. Initial value solutions show that relatively intense vorticity is generated at the sidewall and eventually fills the cylinder with a rotational flew. Although the pressure response is essentially that found in acoustic stability theory, the axial and radial velocity components contain large local radial velocity gradients that cannot be predicted from acoustic theory alone.