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Turbulent energy cascade associated with viscous reconnection of two vortex rings

Authors: 

Van Luc Nguyen, Toai Tuyn Phan, Viet Dung Duong, Nam T. P. Le

Source title: 
Physics of Fluids, 33(8): 085117, 2021 (ISI)
Academic year of acceptance: 
2021-2022
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−3.0at 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.