A Family of Similarity Flows with Vortex Sheets.

by R. C. Alexander

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Prandtl's two-dimensional, time-dependent similarity solutions are corrected and extended to cases of N-branched vortex sheets possessing a certain central symmetry. For both N=1 (Prandtl's case) and N=2 it is found that the similarity parameter m is restricted to the range where m is less than or equal to 1/2. When N=1, multiple solutions are found for a given value of m, provided the absolute value of m is sufficiently small compared to one. A property of these multiple solutions is that the tangential velocity to the concave side of a vortex sheet is 0 exp(-4 pi) smaller than the tangential velocity to the convex side. All values of m are found to be admissible for the case N=3. The flow fields for N=1, 2, and 3 are described in some detail. 36 pp. Ref. (Author)

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