Generation of streamwise helical vortex loops via successive reconnections in early pipe transition

Abstract

We extend the vortex-surface field (VSF), a Lagrangian-based structure identification method, to investigate the vortex reconnection in temporally evolving transitional pipe flows. In the direct numerical simulation (DNS) of round pipe flows, a radial wave-like velocity disturbance is imposed on the inlet region to trigger the transition. The VSF isosurfaces are vortex surfaces composed of vortex lines, and they are concentric tubes with different wall distances at the initial time. The VSF evolution is calculated by the two-time method based on the DNS velocity field, and it is effective to identify the vortex reconnection. In the early stage of transition, the vortex surfaces are first corrugated with streamwise elongated bulges. The escalation and descent of vortex surfaces characterize the generation of high- and low-speed streaks and streamwise vortex pairs, along with the surge of the wall-friction coefficient. The resultant highly coiled and stretched vortex loops then reconnect with each other under the viscous cancelation mechanism. Subsequently, successive vortex reconnections occur via a “greedy snake” mechanism. The streamwise vortex loops consecutively capture the secondary vortex rings pinched off with self-reconnection, forming long helical vortex loops spanning over ten pipe radii in the streamwise direction. Finally, the Kelvin–Helmholtz instability of the shear layer at the trailing edge breaks down the streamwise helical vortex loops into turbulent spots.