Experimental observations from space missions (including more recently Cluster and Time History of Events and Macroscale Interactions during Substorms data) have clearly revealed the existence of high‐speed jets (HSJs) in the downstream region of the quasi‐parallel terrestrial bow shock. Presently, two‐dimensional hybrid simulations are performed in order to investigate the formation of such HSJs through a rippled quasi‐parallel shock front. The simulation results show that (i) such shock fronts are strongly nonstationary along the shock normal, and (ii) ripples are evidenced along the shock front as the upstream ULF waves (excited by interaction between incident and reflected ions) are convected back to the front by the solar wind and contribute to the rippling formation. Then, these ripples are inherent structures of a quasi‐parallel shock. As a consequence, new incident solar wind ions interact differently at different locations along the shock surface, and the ion bulk velocity strongly differs locally as ions are transmitted downstream. Preliminary results show that (i) local bursty patterns of turbulent magnetic field may form within the rippled front and play the role of local secondary shock; (ii) some incident ion flows penetrate the front, suffer some deflection (instead of being decelerated) at the locations of these secondary shocks, and are at the origin of well‐structured (filamentary) HSJs downstream; and (iii) the spatial scales of HSJs are in a good agreement with experimental observations. Such downstream HSJs are shown to be generated by local curvature effects (front rippling) and the nonstationarity of the shock front itself.