J. Fluid Mech. (2011), vol. 686, pp. 451–483. c  Cambridge University Press 2011 451 doi:10.1017/jfm.2011.340 On the structure of vortex rings from inclined nozzles Trung Bao Le, Iman Borazjani, Seokkoo Kang and Fotis Sotiropoulos† Saint Anthony Falls Laboratory, Department of Civil Engineering, University of Minnesota, Minneapolis, MN 55414, USA (Received 2 April 2011; revised 15 July 2011; accepted 3 August 2011; first published online 26 September 2011) We carry out numerical simulations to investigate the vortex dynamics of laminar, impulsively driven flows through inclined nozzles in a piston–cylinder apparatus. Our simulations are motivated by the need to provide a complete description of the intricate vortical structures and governing mechanisms emerging in such flows as documented in the experiments of Webster & Longmire (Phys. Fluids, vol. 10, 1998, pp. 400–416) and Troolin & Longmire (Exp. Fluids, vol. 48, 2010, pp. 409–420). We show that the flow is dominated by the interaction of two main vortical structures: the primary inclined vortex ring at the nozzle exit and the secondary stopping ring that arises due to the entrainment of the flow into the cylinder when the piston stops moving. These two structures are connected together with pairs of vortex tubes, which evolve from the continuous vortex sheet initially connecting the primary vortex ring with the interior cylinder wall. In the exterior of the nozzle the key mechanism responsible for the breakup of the vortical structure is the interaction of the stronger inclined primary ring with the weaker stopping ring near the longest lip of the nozzle. In the interior of the nozzle the dynamics is governed by the axial stretching of the secondary ring and the ultimate impingement of this ring on the cylinder wall. Our simulations also clarify the kinematics of the azimuthal flow along the core of the primary vortex ring documented in the experiments by Lim (Phys. Fluids, vol. 10, 1998, pp. 1666–1671). We show that the azimuthal flow is characterized by a pair of two spiral saddle foci at the long and short lips of the nozzle through which ambient flow enters and exits the primary vortex core. Key words: vortex dynamics, vortex instability, vortex interactions 1. Introduction Vortex ring formation, instability and breakdown phenomena have been the subject of intense research for many decades because they are ubiquitous in a wide range of natural (see Silver 2006; Dabiri 2009; Le, Borazjani & Sotiropoulos 2010) and engineering flows (for a review, see Toyoda & Hiramoto 2009). Understanding such phenomena is important because the compact structure of a vortex ring (Saffman 1992) can be very effective in enhancing scalar mixing under a variety of flow conditions (Sau & Mahesh 2008). In nature, vortex rings form as the result of impulsive momentum transport due to, say, a volcanic eruption (Silver 2006), the flapping of the caudal fin of an aquatic swimmer (Dabiri 2009), or pulsatile blood flow in the cardiovascular system (Gharib et al. 2006; Le et al. 2010). In the laboratory, † Email address for correspondence: fotis@umn.edu