An investigation of a model of turbulence generation in the wall region of a turbulent boundary layer is made through direct numerical simulations. The model is based on the varicose instability of a streak. First, a laminar boundary layer disturbed by a continuous blowing through a slot is simulated in order to reproduce and further investigate the results reported from the experiments of Acarlar and Smith [J. Fluid Mech. 175, 43 (1987)]. An isolated streak with an inflectional profile is generated that becomes unstable, resulting in a train of horseshoe vortices. The frequency of the vortex generation is equal to the experimental results. Comparison of the instability characteristics to those predicted through an Orr-Sommerfeld analysis are in good agreement. Second, a direct numerical simulation of a turbulent boundary layer is performed to point out the similarities between the horseshoe vortices in a turbulent and a laminar boundary layer. The characteristics of streaks and the vortical structures surrounding them in a turbulent boundary layer compare well with the model streak. The results of the present study show that one mechanism for the generation of horseshoe vortices in turbulent boundary layers is related to a normal inflectional instability of the streaks.