The effusing core at the center of a vortex boundary layer

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Abstract
The flow that results when a potential vortex rotates normal to a stationary horizontal disc is considered. This takes the form of an inward flowing boundary layer on the disc which effuses into, and ultimately forms, the core of the vortex. The pressure on the disc falls sharply toward the vortex axis and, over the boundary layer region, is essentially that of the outer flow. The radius at which the base pressure field first deviates appreciably from that of the interior is defined as r1, the radius of the effusing core. This radius and the pressure coefficient at the disc center, C0(0), are determined from radial pressure measurements on the disc over the range of Reynolds numbers, Re, from 3.0×103 to 3.0×104, where Re is based on the radius and the velocity at the disc edge. Three phases are observed as Re is varied. In the first the flow is laminar, r1∝Re−1/2 and C0(0)+1∝Re. The radius r1 continues to decrease and C0(0) to increase with Re in the second phase (1.0×1044), but faster than in the first, while in the third r1 grows and C0(0) falls. The behavior in the latter phases is thought to reflect a transition to turbulence, but several puzzling features are present and further experiments are necessary.

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