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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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.|
|Group:||Guggenheim Jet Propulsion Center|
|Subject Keywords:||vortex pair, perturbation analysis, normalized velocity, boundary shape, steady state|
|Other Numbering System:|
|Classification Code:||AMS subject classifications. 76C05, 35Q30, 35B20|
|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.|
|Deposited By:||Ruth Sustaita|
|Deposited On:||24 Nov 2010 19:18|
|Last Modified:||27 Jan 2016 22:31|
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