The details of the start-up transient vortex structure that forms near the junction of an impulsively started plate and a stationary plate where a step jump in velocity occurs at the plate surfaces are investigated. Numerical simulations have been conducted in a geometry representative of recent experiments of this flow. The experiments did not have access to data at very early times following the impulsive start, but they did suggest that the flow undergoes transitions from a viscous-dominated phase to an inertia-dominated phase. The numerical simulations presented here are designed to explore the early viscous-dominated transients. The simulations show that when the non-dimensional time, τ = tU2/ν (t is the time that the plate has been in motion and ν is the kinematic viscosity), is less than 100, the development process is dominated by viscous forces. In this regime similarity scaling is used to collapse the data, which scale as $\sqrt{t}$. The simulation results at low τ, when evaluated using entrainment diagrams, show an unsteady transition process consisting of the following stages. Initially, the flow consists of a non-rotating vorticity front with a single critical point for τ < 40. For 40 < τ < 50, the flow has three critical points, two nodes and a saddle. A rotational leading jet head develops for τ > 50 as the outermost node evolves into a spiral focus. The simulations span the viscous range to the inertial range. In the inertial range, for τ > 103, the flow structure scales as t5/6, as was observed in the experiments.
Numerical simulations of the SF6-N2 mixed gas streamer discharge development process