Scaling and instability of a junction vortex

Abstract

This paper details experiments in the region where an impulsively started moving wall slides under a stationary wall. The experiments were conducted over a Reynolds number range of Re_Γ=5×10²–5×10⁵. The length scale for the Reynolds number is defined as the distance the wall has moved from rest and increases during an experiment. Experiments show that for Re_Γ>10³ a vortex forms close to the junction where the moving wall meets the stationary one. The data shows that while the vortical structure is small, in relation to the fixed-apparatus length scale, the size of the vortex normalized with respect to the wall speed and viscosity scales in a universal fashion with respect to Re_Γ. The scaling rate is proportional to t^5/6 when the Reynolds number is large. The kinematic behaviour of the vortex is related to the impulse that the moving wall applies to the fluid and results in a prediction that the transient structure should grow as t^5/6 and the velocity field should scale as t^−1/6. The spatial-growth prediction is in good agreement with the experimental results and the velocity scaling is moderately successful in collapsing the experimental data.For Re_Γ>2×10⁴ three-dimensional instabilities appear on the perimeter of the vortical structure and the flow transitions from an unsteady two-dimensional flow to a strongly three-dimensional vortical structure at Re_Γ≃ 4 × 10⁴. The instability mechanism is centrifugal. The formation and growth of these instability structures and their ingestion into the primary vortex core causes the three-dimensional breakdown of the primary vortex. Two movies are available with the online version of the paper.