Formation and evolution of a hairpin vortex induced by subharmonic sinuous low-speed streaks

Abstract

In this paper, a process of the formation and evolution of hairpin vortices, which originated from the interaction between the spanwise-aligned low-speed streaks with a subharmonic sinuous (SS) oscillation mode, is studied using a direct numerical simulation method in a small periodic local region of an incompressible plane channel flow. The initial artificial perturbations are used to excite the SS-mode oscillation of two spanwise-aligned low-speed streaks in such a flow. A new mechanism of formation and decay of the hairpin vortices is proposed in which the shear layer induced by the spanwise collision and merging between the low-speed streaks is emphasized. Our results show that the streamwise vortices can be induced by the SS-mode streaks and then developed into an X-like pattern at the initial stage due to the mutual induction effect. The X-like vortices further enhance the spanwise oscillation and lift-up of the two streaks that thus lead to the spanwise collision and merging of the low-speed streaks and produce a low-speed region in high-speed fluid. The strong shear layer between the high- and low-speed fluids gives rise to the spanwise vorticity that connects the X-like streamwise vortices and forms the Λ-like vortex. Once the low-speed region entirely enters the high-speed fluid, the shear layer shows the ring shape and results in the transition from a Λ-like vortex to Ω-like one. After that, the viscous diffusion of the low-speed region in the high-speed fluid leads to the decay of the Ω-like vortex; the collision and merging of the low-speed streaks simultaneously reoccur upstream and give birth to a secondary Λ-like vortex, which exhibits behavior that is nearly similar with that of the primary one. Although the hairpin vortex packet is not observed in the present plane channel flow, the regeneration of the hairpin vortex suggests that this type of vortical structure plays an important role in the wall-bounded flow.