Influence of step height on the secondary instability in a boundary layer over backward-facing step

The development of secondary instabilities is investigated numerically for a zero pressure-gradient transitional boundary layer over a backward-facing step at Re_δ*o = 1000. Two step heights are considered in this work, namely, h/δ*_o = 0.5 and 1.0 (δ*_o denotes the displacement thickness evaluated at the step location). Small disturbances are introduced by periodic blowing and suction through the wall within a narrow ribbon. A well-resolved direct numerical simulation (DNS) is carried out for the two cases to characterize the laminar-turbulent transition. The results for the h/δ*_o = 1.0 case show a rapid transition due to the Kelvin-Helmholtz (K–H) instability downstream of step such that the non-linear interactions already occur within the recirculation region, and the flow pattern loses its mirror-symmetry in the middle stage of transition.  In contrast, case h/δ*_o = 0.5 presents a  transition road map in which transition occurs far downstream of the step and the coefficient of skin-friction, C_f, demonstrates different slopes before the `over-shoot' is reached. Mirror-symmetry holds till close to the late stage of transition.