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2013
Impact Factor

Kevin O'Neil

800 Tucker Dr., Tulsa OK 74104 USA
University of Tulsa

Publications:

O'Neil K. A.
Relations Satisfied by Point Vortex Equilibria with Strength Ratio $-2$
2018, vol. 23, no. 5, pp.  580-582
Abstract
Relations satisfied by the roots of the Loutsenko sequence of polynomials are derived. These roots are known to correspond to families of stationary and uniformly translating point vortices with two vortex strengths in ratio $-2$. The relations are analogous to those satisfied by the roots of the Adler–Moser polynomials, corresponding to equilibria with ratio $-1$. The proof uses an analysis of the differential equation that these polynomial pairs satisfy.
Keywords: point vortex, polynomial, equilibrium
Citation: O'Neil K. A.,  Relations Satisfied by Point Vortex Equilibria with Strength Ratio $-2$, Regular and Chaotic Dynamics, 2018, vol. 23, no. 5, pp. 580-582
DOI:10.1134/S1560354718050076
O'Neil K. A.
Dipole and Multipole Flows with Point Vortices and Vortex Sheets
2018, vol. 23, no. 5, pp.  519-529
Abstract
An exact method is presented for obtaining uniformly translating distributions of vorticity in a two-dimensional ideal fluid, or equivalently, stationary distributions in the presence of a uniform background flow. These distributions are generalizations of the well-known vortex dipole and consist of a collection of point vortices and an equal number of bounded vortex sheets. Both the vorticity density of the vortex sheets and the velocity field of the fluid are expressed in terms of a simple rational function in which the point vortex positions and strengths appear as parameters. The vortex sheets lie on heteroclinic streamlines of the flow. Dipoles and multipoles that move parallel to a straight fluid boundary are also obtained. By setting the translation velocity to zero, equilibrium configurations of point vortices and vortex sheets are found.
Keywords: point vortex, vortex sheet, equilibrium, dipole
Citation: O'Neil K. A.,  Dipole and Multipole Flows with Point Vortices and Vortex Sheets, Regular and Chaotic Dynamics, 2018, vol. 23, no. 5, pp. 519-529
DOI:10.1134/S1560354718050039
O'Neil K. A.
Point Vortex Equilibria Related to Bessel Polynomials
2016, vol. 21, no. 3, pp.  249-253
Abstract
The method of polynomials is used to construct two families of stationary point vortex configurations. The vortices are placed at the reciprocals of the zeroes of Bessel polynomials. Configurations that translate uniformly, and configurations that are completely stationary, are obtained in this way.
Keywords: point vortex, equilibrium, polynomial method
Citation: O'Neil K. A.,  Point Vortex Equilibria Related to Bessel Polynomials, Regular and Chaotic Dynamics, 2016, vol. 21, no. 3, pp. 249-253
DOI:10.1134/S1560354716030011

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