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The flow in the neighbourhood of the rim of a finite rotating disc
Author(s) -
Smith S. H.
Publication year - 1973
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300003612
Subject(s) - wake , ekman number , trailing edge , ekman layer , mathematics , flow (mathematics) , geometry , deck , neighbourhood (mathematics) , mechanics , boundary layer , geology , mathematical analysis , physics , oceanography
The flow in the wake of a finite rotating disc was recently investigated by Leslie [1], who showed that the structure of the wake was very similar to that found for the two‐dimensional flow past the trailing edge of a flat plate by Goldstein. Here, we investigate the inner region where the Goldstein wake joins onto the flow over the plate itself. Because there is no pressure jump across the rim at the edge of the Ekman layer, no third deck is necessary, so this inner region has width O ( E ½ ) and contains just two decks, the lower thickness O ( E ⅔ ) and the upper with thickness O ( E ½ ); E is the Ekman number for the flow. The resultant differential equation in the lower deck for the radial and axial velocities is uncoupled from that for the azimuthal velocity, and has exactly the same form as the equation found by Stewartson [4] for the lower deck in the flat plate problem cited above.