Direct numerical simulations have been conducted to examine the evolution of eddies in the presence of large-scale shear flows. The numerical experiments consist of initial-value-problems in which monopolar and dipolar vortices as well as driven turbulence are superposed on a plane Couette or Poiseuille flow in a periodic two-dimensional channel. The evolution of the flow has been examined for different shear rates of the background flow and different widths of the channel. Results found for retro-grade and pro-grade monopolar vortices are consistent with those found in the literature. Boundary layer vorticity, however, can significantly modify the straining and erosion of monopolar vortices normally seen for unbounded domains. Dipolar vortices are shown to be much more robust coherent structures in a large-scale shear flow than monopolar eddies. An analytical model for their trajectories, which are determined by self-advection and advection and rotation by the shear flow, is presented. Turbulent kinetic energy is effectively suppressed by the shearing action of the background flow provided that the shear is linear (Couette flow) and of sufficient strength. Nonlinear shear as present in the Poiseuille flow seems to even increase the turbulence strength especially for high shear rates.