Turbulent energy cascade associated with viscous reconnection of two vortex rings

Abstract

Collision of two vortex rings (VR) initially arranged in axis-offset and orthogonal configurations at Reynolds numbers (ReΓ) in the range of 5000–200 000 was simulated to investigate turbulent energy cascade associated with their reconnection. Two elliptical VRs are generated by joining each part of the first VR with another part of the second VR for the axis-offset collision, while two VRs associate to form a double U-shaped vortex, and this vortex reconnects itself at two points to form three elliptical VRs linked by the vortex filaments for the orthogonal collision. Many vortex structures in various scales and shapes, including small-scale VRs and horseshoe vortices, are observed in connection regions for both cases. As ReΓ increases, the energy of formed small vortices raises and their wavenumber (k) range enlarges. The flow energy spectrum approaches a k−5/3 slope of the Kolmogorov hypotheses at low wavenumbers. For the axis-offset collision, the energy spectrum at medium wavenumbers continuously changes from k−3.0 at ReΓ= 5000 to k−1.8 at ReΓ= 200 000, and the exponent (α) of the wavenumber is determined by a function as α=0.3304 ln(ReΓ)−5.6538. Meanwhile, the energy spectrum at two medium-wavenumber subranges for the orthogonal collision with ReΓ≥ 20 000 approaches the slopes of k−3.0 and k−2.6. Turbulent mixing performance due to the axis-offset collision of two vortex rings is better than that with the orthogonal one.

On the stability of a pair of vortex rings

“…Finally, while the present work concerns the direct collision of two vortex rings approaching from an initially large separation distance, the analysis for an expanding vortex dipole formed from a radially diverging annular starting jet is identical, with an appropriate definition of the vortex cores in the dipole. Given the difficulties associated with precisely aligning two vortex ring generators for a direct collision, the latter may be a convenient, and possibly more controllable, experimental set-up for examining the vortex core interactions that are the subject of many recent studies (Brenner et al 2016;McKeown et al 2018McKeown et al , 2020Mishra et al 2021;Nguyen et al 2021;Qi et al 2022). Moreover, the growth of the CI along an annular starting jet may be relevant to certain astrophysical systems.…”

“…Later, the CI and the formation of secondary vortex rings were observed in experiments of colliding coaxial vortex rings of equal strength (Lim & Nickels 1992), spurring subsequent studies of the phenomenon examining the evolution of enstrophy during different stages of the ring collision (Chu et al 1995), compressibility (Minota, Nishida & Lee 1998) and numerical requirements for accurate simulation (Mansfield, Knio & Meneveau 1999). More recently, this canonical flow was used to study vortex interactions and the generation of scales leading up to the transition to turbulence, in particular the emergence of a turbulent puff beyond a critical Reynolds number, in a variety of theoretical (Lu & Doering 2008;Brenner, Hormoz & Pumir 2016), experimental (Lu & Doering 2008;Brenner et al 2016;McKeown et al 2018McKeown et al , 2020 and computational studies (Mishra, Pumir & Ostilla-Mónico 2021;Nguyen et al 2021;Arun & Colonius 2023).…”

“…2018, 2020) and computational studies (Mishra, Pumir & Ostilla-Mónico 2021; Nguyen et al. 2021; Arun & Colonius 2023).…”

Velocity gradient analysis of a head-on vortex ring collision

“…Collisions between vortex rings and other vortex rings, walls and free surfaces are also commonly studied to investigate mechanisms underlying the turbulent cascade and the generation of small scales (see Mishra, Pumir & Ostilla-Mónico (2021) for a review). These mechanisms can be characterized using a variety of collision geometries, including head-on collisions (Cheng, Lou & Lim 2018;McKeown et al 2018McKeown et al , 2020Mishra et al 2021), inclined collisions (Kida, Takaoka & Hussain 1991;Yao & Hussain 2020a,c) and axis-offset collisions (Zawadzki & Aref 1991;Smith & Wei 1994;Nguyen et al 2021), among others. Boundary layers play an important role in vortex-wall interactions (e.g.…”

“…2021), inclined collisions (Kida, Takaoka & Hussain 1991; Yao & Hussain 2020 a , c ) and axis-offset collisions (Zawadzki & Aref 1991; Smith & Wei 1994; Nguyen et al. 2021), among others. Boundary layers play an important role in vortex–wall interactions (e.g.…”