On the stages of vortex decay in an impulsively stopped, rotating cylinder

Abstract

The flow within an infinitely long cylinder exhibiting solid-body rotation (SBR) is impulsively stopped. The complete decay of the initial SBR is captured by means of direct numerical simulations for a wide range of Reynolds numbers ( $Re$ ). Five distinct stages are identified during the decay process according to their flow structure and their underlying mechanisms of kinetic-energy dissipation. Initially, the laminar boundary layer undergoes a primary centrifugal instability, which causes the formation of coherent Taylor rolls. The flow then becomes turbulent, once the Taylor rolls are corrupted by secondary instabilities. Within the turbulent stage, two phases are distinguished. In the first turbulent phase, the SBR core is still intact and turbulence is sustained. The mean velocity profile is well described by the superposition of a near-wall region, a retracting SBR core and an intermediate region of constant angular momentum. In the latter region, the magnitude of angular momentum in viscous units $l^{+}(Re)$ is approximately constant in time. In the second turbulent phase, the SBR core breaks down, turbulence starts to decay exponentially and the kinetic energy of the mean flow decays logarithmically. Eventually, the flow relaminarises and the velocity profile of the analytical solution for purely laminar decay is recovered, albeit at an earlier temporal instant due to the net effect of transition and turbulence.