Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published February 1994 | Published
Journal Article Open

The Steady Motion of a Symmetric, Finite Core Size, Counterrotating Vortex Pair

Abstract

The steady motion of a symmetric, finite core size, counterrotating vortex pair is characterized by circulation r, a velocity V, and a spacing 2x_∞. In the classical limit of a point vortex, the normalized velocity, vx_∞/r, is 1/(4π). The effect of finite core size is to reduce the normalized velocity below the value for a point vortex. The flow is governed by a single geometrical parameter R/x_∞, the ratio of effective vortex size to vortex half-spacing. Perturbation analysis is used to derive general, closed-form analytical solutions for the complete velocity field, the vortex pair velocity, and the boundary shape for a continuum of values of R/x_∞. Both uniform and piecewise constant density cases are treated. These solutions illustrate the different orders at which the solution deviates from the point vortex pair. For example, the vortex shape becomes noncircular at order (R/x_∞)^2, but the normalized velocity does not change until order (R/x_∞)^5. For the uniform density case, calculation of specific values of vortex pair velocity, aspect ratio, and gap ratio shows good agreement with previous numerical results.

Additional Information

© 1994 Society for Industrial and Applied Mathematics. Received by the editors November 30, 1992; accepted for publication (in revised form) March 16 1993. T his work was supported by U.S. Air Force Office of Scientific Research contract F49620-86-C-0113 and grant AFOSR-90-0188. The first author was supported by an Office of Naval Research Graduate Fellowship.

Attached Files

Published - 358_Joseph_Y_1994.pdf

Files

358_Joseph_Y_1994.pdf
Files (428.7 kB)
Name Size Download all
md5:2cf633b80a63a5f50441efe1d115bff0
428.7 kB Preview Download

Additional details

Created:
August 20, 2023
Modified:
October 20, 2023