# Accession Number:

## AD0707036

# Title:

## A FAMILY OF SIMILARITY FLOWS WITH VORTEX SHEETS,

# Descriptive Note:

# Corporate Author:

## RAND CORP SANTA MONICA CALIF

# Personal Author(s):

# Report Date:

## 1970-05-01

# Pagination or Media Count:

## 33.0

# Abstract:

Prandtls 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 Prandtls case and N 2 it is found that the similarity parameter m is restricted to the range m or 12. 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 0exp-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:

# Subject Categories:

- Aerodynamics
- Fluid Mechanics