ONE MECHANISM OF HAIRPIN VORTEX GENERATION BASED ON STREAK TRANSIENT GROWTH

The vortical structures due to the streak transient growth is studied by direct numerical simulations of the minimal channel flow at Reτ = 400. The streak profile is obtained by conditional averaging the DNS data of fully developed turbulent channel flow, in which the linearly stable streaks are prevailing. Therefore, the stable streak with moderate strength is selected and the sinuous perturbation of spanwise velocity is imposed initially. The generation of a complete hairpin vortex structure as well as the hairpin packet is observed. The mechanism for the formation of hairpin vortex is analyzed by using the vorticity transport equation along the vortex lines. The stretching and titling of the vortex lines play a significant role in the generation of the hairpin vortex. INTRODUCTION Coherent structures commonly exist and play significant roles in wall turbulence. Earlier flow visualization using hydrogen bubbles, dyes, or smoke (e.g. Kline et al., 1967; Head & Bandypoyadhyay, 1981), discovered low speed streaks and burst events in the nearwall region. Recently, the three dimensional coherent structures, i.e., hairpin or horseshoe vortex embedded in the instantaneous velocity fields were directly identified by PIV measurements (Meinhart & Adiran, 1995; Adrian et al., 2000; Gao et al., 2011) besides the evidence for the existence of hairpin vortices given by direct numerical simulations (Robinson, 1991; Zhou & Adrian, 1999; Wu & Moin, 2009). Furthermore, it was demonstrated that the hairpin vortices were also present in homogeneous shear turbulence, which is free of solid wall (Supomotsky et al., 2005; Vanderwel & Tavoularis, 2011). The individual hairpin vortex was proposed by Theodorsen (1952), refers to an Ω -shaped vortical structure with two streamwise-oriented legs connected via a raised, spanwise-oriented arch. The hairpin vortices are predominant on side and appear with their heads pointing downstream and towards the high-velocity fluid (Robinson, 1991). They always formed and travelled in groups, resulting in local zones of low momentum fluid (Meinhart & Adrian, 1995; Adrian et al., 2000). Hairpin vortices make a major contribution to the Reynolds stresses and turbulence transport (Adrian, 2007; Lee & Sung, 2011). The scales and shapes in different time period and position away from the wall were described by Robinson (1991), Zhou et al. (1999) and Adrian (2007). The near-wall cycle provided a well explanation for turbulence regeneration and sustaining in low-Reynolds number wall turbulence (Jimenez & Moin, 1991). As the Reynolds number increases, the large-scale motions in the logarithmic region become increasingly comparable in energy possession to the near-wall cycle (Balakumar & Adrian, 2007; Hutchins & Marusic, 2007). The hairpin packet is considered as an interpretation to the origin of the large-scale motion in the outer layer (Adrian, 2007). However, the mechanisms of hairpin vortex generation and their formation in groups are still lack of universal knowledge. The presently proposed mechanisms for hairpin vortex generation can be categorized into parentoffspring and instability-based scenarios. On the former scenario, Smith & Walker (1994) proposed that the parent hairpin produces localized ejections near its head and legs, and the resulting inflectional shear flow then rolls up by Kelvin-Helmholtz instability and gives birth to new hairpins. Zhou et al. (1999) showed that the sufficiently strong Q2 event could develop into the primary hairpin vortex and induce the following downstream, secondary and tertiary hairpin vortex, which presents a scenario of hairpin packet generation. On the latter scenario, Skote et al. (2002) concentrated on the streak instability and suggested that hairpin vortices are related to the varicose type perturbation, while sinuous type collision leads to streamwise vortex generation. Schoppa & Hussain (2000) found the streak can lead to spanwise ‘arch’ vortices generation based on sinuous instability in near-wall turbulence. In the present study, we will present a hairpin generation mechanism based on streak sinuous instability. Using the streak profile obtained by conditional averaging the DNS data of turbulent channel flow at Reτ = 400, the generation of a complete hairpin vortex structure as well as the hairpin packet was observed. The mechanism was analyzed by using the vorticity transport equation along