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

Yang, Joseph and Kubota, Toshi (1994) The Steady Motion of a Symmetric, Finite Core Size, Counterrotating Vortex Pair. SIAM Journal on Applied Mathematics, 54 (1). pp. 14-25. ISSN 0036-1399. http://resolver.caltech.edu/CaltechAUTHORS:20101123-110851054

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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.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1137/S0036139992240917DOIUNSPECIFIED
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. This 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.
Group:Guggenheim Jet Propulsion Center
Funders:
Funding AgencyGrant Number
U.S. Air Force Office of Scientific ResearchF49620-86-C-0113
U.S. Air Force Office of Scientific ResearchAFOSR-90-0188
Office of Naval Research Graduate FellowshipUNSPECIFIED
Subject Keywords:vortex pair, perturbation analysis, normalized velocity, boundary shape, steady state
Other Numbering System:
Other Numbering System NameOther Numbering System ID
Guggenheim Jet Propulsion Center358
Classification Code:AMS subject classifications. 76C05, 35Q30, 35B20
Record Number:CaltechAUTHORS:20101123-110851054
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20101123-110851054
Official Citation:The Steady Motion of a Symmetric, Finite Core Size, Counterrotating Vortex Pair Joseph Yang and Toshi Kubota, SIAM J. Appl. Math. 54, 14 (1994), DOI:10.1137/S0036139992240917
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:20981
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:24 Nov 2010 19:18
Last Modified:26 Dec 2012 12:40

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