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Linear growth rates of types I and II convective modes within the rotating-cone boundary layer

By S.J. Garrett


This paper was published as Fluid Dynamics Research, 2010, 42 (2), 5504. It is available from Doi: 10.1088/0169-5983/42/2/025504Metadata only entryExperimental observations have shown that the transition characteristics of the boundary-layer flow over rotating cones depends on the cone half-angle. In particular, pairs of counter-rotating Görtler-type vortices are observed over cones with slender half-angles and co-rotating vortices are observed over broad cones. Garrett et al (2009 J. Fluid Mech. 622 209–32) have hypothesized the existence of a centrifugal instability mode over slender cones that is more dangerous than the types I (crossflow) and II (streamline curvature) modes which dominate over rotating disks and broad cones. Work is currently underway to clarify this alternative mode; however, a clear understanding of the growth rates of types I and II modes is crucial to the ultimate understanding of how the dominant mode changes with half-angle. In this paper, we demonstrate that the maximum growth rate for types I and II modes decreases with reduced half-angle, which clears the way for the dominance of the alternative instability mode. Furthermore, it is suggested that vortices travelling at 75% of the cone surface speed will be selected over smooth, clean rotating cones with half-angle such that the type I mode is dominant. Interestingly, this vortex speed has been experimentally observed by Kobayashi and Arai within the rotating-sphere boundary layer

Publisher: IOP Publishing on behalf of the Japan Society of Fluid Mechanics
Year: 2010
DOI identifier: 10.1088/0169-5983
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