Accession Number : AD0707036

Title :   A FAMILY OF SIMILARITY FLOWS WITH VORTEX SHEETS,

Corporate Author : RAND CORP SANTA MONICA CALIF

Personal Author(s) : Alexander,R. C.

Report Date : MAY 1970

Pagination or Media Count : 33

Abstract : 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 m = or < 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. In all cases it is found that certain features of the flows resemble a classical (but time-dependent) circular vortex. For example, it is found that the circulation in a disk of radius r is proportional to r squared. There are also important differences. The flow fields for N = 1, 2, and 3 are described in some detail. (Author)

Descriptors :   (*TWO DIMENSIONAL FLOW, BOUNDARY VALUE PROBLEMS), (*VORTICES, FLOW VISUALIZATION), PARTIAL DIFFERENTIAL EQUATIONS, EQUATIONS OF MOTION, GRAPHICS

Subject Categories : Aerodynamics
      Fluid Mechanics

Distribution Statement : APPROVED FOR PUBLIC RELEASE