Formation of surface trailing counter-rotating vortex pairs downstream of a sonic jet in a supersonic cross-flow

Direct numerical simulations were conducted to uncover physical aspects of a transverse sonic jet injected into a supersonic cross-flow at a Mach number of 2.7. Simulations were carried out for two different jet-to-cross-flow momentum flux ratios of 2.3 and 5.5. It is identified that collision shock waves behind the jet induce a herringbone separation bubble in the near-wall jet wake and a reattachment valley is formed and embayed by the herringbone recirculation zone. The recirculating flow in the jet leeward separation bubble forms a primary trailing counter-rotating vortex pair (TCVP) close to the wall surface. Analysis on streamlines passing the separation region shows that the wing of the herringbone separation bubble serves as a micro-ramp vortex generator and streamlines acquire angular momentum downstream to form a secondary surface TCVP in the reattachment valley. Herringbone separation wings disappear in the far field due to the cross-interaction of lateral supersonic flow and the expansion flow in the reattachment valley, which also leads to the vanishing of the secondary TCVP. A three-dimensional schematic of surface trailing wakes is presented and explains the formation mechanisms of the surface TCVPs.