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

  • Frieder Kaiser (a1), Bettina Frohnapfel (a1), Rodolfo Ostilla-Mónico (a2), Jochen Kriegseis (a1), David E. Rival (a3) and Davide Gatti (a1)...


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.

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Kaiser et al. supplementary movie 1
Transition to turbulence for Re=12000: (a) boundary-layer thickness and wall-shear stress; (b) turbulent and mean kinetic energy; (c) energy distribution inside the boundary layer, red dashed line marks the critical wavenumber. The purple line in (a,b,c) depicts the time instance visualized in (d,e). The vertical dashed lines are described in the manuscript in figure 7; (d) one-dimensional spectrum inside the boundary layer. The black dashed-dotted line marks the critical wavenumber for Re=12000, the orange line marks the wavenumber, which would be the most energetic wavenumber if the streamwise vortices were circular and would extend over the boundary-layer thickness; and (e) velocity fluctuations. The orange line marks the boundary-layer thickness, red line (appears after transition to turbulence) marks the inner limit of the region of constant angular momentum.

 Video (13.4 MB)
13.4 MB

Kaiser et al. supplementary movie 2
FTLE visualisations of the transition process to turbulence at Re = 12000.

 Video (5.2 MB)
5.2 MB

Kaiser et al. supplementary movie 3
(a,b) Mean velocity profile and Reynolds stresses in outer (a) and wall-based (b) units. (c,d) Terms of the mean (c) and turbulent (d) kinetic energy budget equations.

 Video (3.3 MB)
3.3 MB

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

  • Frieder Kaiser (a1), Bettina Frohnapfel (a1), Rodolfo Ostilla-Mónico (a2), Jochen Kriegseis (a1), David E. Rival (a3) and Davide Gatti (a1)...


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