To acquire insight into the role of free-stream turbulence on laminar-turbulent transition, the interaction between a boundary layer and an array of single-wavenumber vortices convected at the mean free-stream velocity is studied analytically and numerically. For small amplitudes, the effect of a spectrum can be obtained by superposition. The flow field is taken to be the sum of the steady laminar field (Blasius) plus a flow field ascribable to the effects of the vortex array. This latter flow field is further subdivided into the portion that exists in the absence of the plate (the vortex array itself) plus a flow field representing the alteration to that array due to the shearing mean flow and no-slip and impermeability conditions at the plate surface. This last portion of the flow field is described by a nonhomogeneous Orr–Sommerfeld equation with phase speed unity and real wavenumber. The forcing function depends on the mean flow and on the free-stream disturbance array. The problem is not an eigenvalu...