Three-dimensional wave structure within the puff of pipe flow

Direct numerical simulations are conducted to investigate the puff in pipe flow at various Reynolds numbers. Lagrangian approaches and vortex dynamics analysis are employed to examine the early-stage flow structures. The formation of low-speed streaks and the lift-up of three-dimensional (3D) waves (which is the same as soliton-like coherent structures in the boundary layer) upstream of the puff are observed in a pipe flow using timeline visualizations. The instantaneous vorticity deviation criterion reveals hairpin vortices surrounding 3D waves within the flow field. Vortex formation consistently follows 3D wave development, with the spatial delay influenced by the wave amplitude. The effects of the Reynolds number on the turbulence dynamics are assessed.