Erratum: Sheet, ligament and droplet formation in swirling primary atomization (AIP Advances (2018) 8 (045211) DOI: 10.1063/1.5079830)

We realized some relevant studies had not been well referenced, and would like to amend the paper by an erratum as follows. In the introduction part,1 statements should have been added as "Jarrahbashi and Sirignano2 firstly investigated the ligament formation of round straight jet from the perspective of vorticity dynamics. By using the λ2 approach to identify the vortex structures and the level set method to capture the interface, they found that counter-rotating and streamwise vortices contribute to the ligament formation even for jets flowing into like-density fluid. Furthermore, by investigating round liquid jet with coaxial gas flow, Jarrahbashi et al.3 found the formation mechanisms of smaller structures, such as lobes, holes, bridges and ligaments are associated with the interaction between wave dynamics and vortex dynamics for different gas-to-liquid density ratio, liquid Reynolds number and liquidWeber number. Zandian et al.4 investigated three-dimensional instabilities on a planar liquid sheet and summarized three atomization cascades based on the gas Weber number and liquid Reynolds number. Three distinct physical domains were also identified. These studies provided newinsights of small structures formation considering of vortex dynamics and it is interesting to investigate whether it is valid for the present swirling breakup."