Spectral direct numerical simulations (DNS) are carried out for a source–sink flow in an annular cavity between two co-rotating disks. When the Reynolds number based on the forced inflow is increased, a self-sustained crossflow instability of finite amplitude is observed. We show that this nonlinear global mode is made up of a front located at the upstream boundary of the absolutely unstable domain, followed by a saturated spiral mode, and that its properties are in good agreement with results of the local stability theory. This structure is characteristic of the so-called elephant mode of Pier & Huerre (J. Fluid Mech. vol. 435, 2001, p. 145). The global bifurcation is subcritical since only large-amplitude initial perturbations are found to trigger the elephant mode. Small-amplitude perturbations induce a long-lasting transient growth but lead eventually to a damped linear global mode, showing that non-parallel effects counteract the absolute instability and restabilize the flow. A similar linear global stabilization due to non-parallel effects has been found in the case of the flow above a single rotating disk. For the single-disk geometry, the existence of an elephant mode would imply, together with results of Davies & Carpenter (2003) a subcritical global instability, which has not yet been demonstrated. Although the present geometry differs from the single-disk case, the existence of a subcritical global bifurcation is now established, allowing a precise analysis of the transition scenarios.

We report an analysis of small-scale enstrophy ω2 and rate of strain s2 dynamics in the proximity of the turbulent/non-turbulent interface in a flow without strong mean shear. The techniques used are three-dimensional particle tracking (3D-PTV), allowing the field of velocity derivatives to be measured and followed in a Lagrangian manner, and direct numerical simulations (DNS). In both experiment and simulation the Taylor-microscale Reynolds number is Reλ = 50. The results are based on the Lagrangian viewpoint with the main focus on flow particle tracers crossing the turbulent/non-turbulent interface. This approach allowed a direct investigation of the key physical processes underlying the entrainment phenomenon and revealed the role of small-scale non-local, inviscid and viscous processes. We found that the entrainment mechanism is initiated by self-amplification of s2 through the combined effect of strain production and pressure--strain interaction. This process is followed by a sharp change of ω2 induced mostly by production due to viscous effects. The influence of inviscid production is initially small but gradually increasing, whereas viscous production changes abruptly towards the destruction of ω2. Finally, shortly after the crossing of the turbulent/non-turbulent interface, production and dissipation of both enstrophy and strain reach a balance. The characteristic time scale of the described processes is the Kolmogorov time scale, τη. Locally, the characteristic velocity of the fluid relative to the turbulent/non-turbulent interface is the Kolmogorov velocity, uη.