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Transition near the edge of a rotating disk

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The three-dimensional boundary layer due to a disk rotating in otherwise still fluid is known for its robust laminar-turbulent transition occurring at a non-dimensional radius Rt ≃ 500, closely corresponding to the onset of local absolute instability at Rca ≃ 507. Assuming a disk of infinite extent, previous studies have established the global linear stability of the base boundary-layer flow, while the nonlinear behaviour can be explained by a scenario involving
both local primary and secondary absolute instabilities. Indeed, local absolute instability is only a necessary but not a sufficient condition for global linear instability. In contrast, nonlinear global modes (aka “elephant” global modes) are triggered by a sharp front at the transition from local convective to absolute instability; thus, the existence of local absolute instability is a necessary and sufficient condition for global nonlinear instability. It turns out that the rotating-disk flow precisely falls into the category of linearly stable but nonlinearly unstable systems.

Author(s):

Benoît Pier    
Laboratoire de mécanique des fluides et d'acoustique (CNRS-Université de Lyon)
France