Instability and transition in the boundary layer driven by a rotating slender cone. (31st March 2021)

• Record Type: Journal Article
• Authors: Kato, K.; Segalini, A.; Alfredsson, P.H.; Lingwood, R.J.
• Is Part Of: Journal of fluid mechanics. Volume 915(2021)
• Publication Date: 2021-03-31
• Subjects: transition to turbulence; Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2021.216
• Languages: English
• ISSNs: 0022-1120

Abstract

Abstract: Abstract : Instability and transition in the boundary layer on a slender cone ( $60^{\circ }$ apex angle) rotating in still fluid are investigated using hot-wire anemometry as well as through linear stability analysis. In contrast to broad cones (including the disk), where a cross-flow instability dominates the transition and different studies report similar transition Reynolds numbers, the reported transition Reynolds numbers on slender cones are scattered. The present experiments provide quantitative experimental datasets and the stability and transition are evaluated based on both the Reynolds number and a Görtler number. The results consistently show that the instability development depends on the Görtler number rather than the Reynolds number and that transition starts at a well-defined Görtler number, whereas the transition Reynolds number depends on the rotational rate. The measured disturbance that first grows in the laminar region has a frequency approximately the same as or twice the rotational rate of the cone, which according to the stability analysis corresponds to the critical frequency of a slightly inclined vortex structure with respect to the cone axis or an axisymmetric vortex structure. These structures are similar to those observed in the flow visualisations of Kobayashi & Izumi ( J. Fluid Mech., vol. 127, 1983, pp. 353–364) and considered as being due to a centrifugal instability.