Formation number and pinch-off signals of disc vortex ring based on a Lagrangian analysis

Abstract

As one fundamental flow structure, the vortex ring behind an impulsively starting disc can vividly characterize the vortex structure around the flapping flight and the drag-based paddling propulsions. In this paper, an elaborate experiment is performed to investigate the formation of the vortex rings (termed as DVR) by using digital particle image velocimetry (DPIV), as well as by investigating the ridges of finite-time Lyapunov exponent (FTLE) and the elliptic Lagrangian coherent structures (LCSs). Experimental results demonstrate that the circulation growth of DVRs satisfies the Logistic law and can be well predicted by a scaling model based on the shear-layer feeding velocity. Applying the criterion originated from the Kelvin-Benjamin variational principle, the formation number of DVRs when DVRs pinch off is found to stay within the range of F∗=3.35~4.1. Then, the pinch-off process of the DVRs is re-examined based on a Lagrangian analysis, and the dynamic signals are detected to coincide with the onset of DVRs pinch-off. Once DVRs pinch off, a trailing pressure maximum appears in the edge of disc and a closed boundary forms to define the region of DVRs based on the FTLE ridges, fluid detrainment by the dynamic lobes is observed, and a saturation phase of the circulation evolution is clearly observed in terms of the elliptic LCSs. Furthermore, the scaling laws, i.e., circulation growth and formation number, of DVR formation suggest a confined formation mode to understand the formation of wake vortices behind a moving body for reference.