The effusing core at the center of a vortex boundary layer
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 r_{1}, the radius of the effusing core. This radius and the pressure coefficient at the disc center, C_{0}(0), are determined from radial pressure measurements on the disc over the range of Reynolds numbers, Re, from 3.0×10^{3} to 3.0×10^{4}, 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, r_{1}∝Re^{}^{1}^{/}^{2} and C_{0}(0)+1∝Re. The radius r_{1} continues to decrease and C_{0}(0) to increase with Re in the second phase (1.0×10^{4}<Re<1.55×10^{4}), but faster than in the first, while in the third r_{1} grows and C_{0}(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.
 Publication:

Physics of Fluids
 Pub Date:
 September 1984
 DOI:
 10.1063/1.864900
 Bibcode:
 1984PhFl...27.2215P
 Keywords:

 Boundary Layer Flow;
 Core Flow;
 Laminar Flow;
 Transition Flow;
 Turbulent Flow;
 Vortices;
 Disks (Shapes);
 Flow Distribution;
 Integral Equations;
 Pressure Distribution;
 Reynolds Number;
 Spherical Coordinates;
 Fluid Mechanics and Heat Transfer