The goal is to adapt a nonreflecting outlet boundary condition, derived from a wave equation, to the numerical solution of the full incompressible Navier-Stokes equations, for an elliptic unsteady free shear flow. The physical phenomena studied concern the onset of the Kelvin-Helmholtz instability in the free (non-forced) shear layer and certain 2D characteristics of transition towards turbulence. Owing to the nonreflecting boundary conditions, the feedback noises are inhibited effectively, so that the computation domain can be reduced and the dynamic characteristics of the flow are maintained up clearly to the outlet boundary.