Lagrangian analysis of the fluid transport induced by the interaction of two co-axial co-rotating vortex rings

Abstract

In this paper, the fluid transport in the interaction of two co-axial co-rotating vortex rings are investigated. Vortex rings are generated using the piston-cylinder apparatus, and the resulting velocity fields are measured using digital particle image velocimetry. The interaction process is analysed by means of vorticity contour, as well by investigation of the Lagrangian coherent structures (LCSs) defined by the ridges of the finite-time Lyapunov exponent (FTLE). Experimental results demonstrate that two types of vortex interaction are identified, namely strong and weak interactions, respectively. For the strong interaction, the Lagrangian boundaries of the two vortex rings are merged together and form a flux window for fluid transport. For weak interaction, only the Lagrangian drift induced by the motion of the front vortex ring is observed and affects the Lagrangian boundary of the rear vortex ring. Moreover, the fluids transported in the strong interaction carry considerable momentum but no circulation. By contrast, there are nearly no fluxes occurring in the weak interaction. By tracking the variations of circulation and impulse occupied by the separated regions distinguished by the LCSs, it is found that the circulation nearly has no change, but the impulse occupied by vortex core region has significant change. In the strong interaction, the impulse of rear vortex ring decreases but the impulse of the front vortex ring increases. Based on the impulse law, it is speculated that the fluid force generated by the formation of the rear vortex rings can be enhanced. Therefore, the strong interaction between wake vortices can actually improve the propulsive efficiency of the biological systems by operating the formation of large-scale vortices.