Equilibrium vortex configurations in domains with boundary

Miller, Kenneth G.

doi:10.1090/qam/1632318

Author: Kenneth G. Miller
Journal: Quart. Appl. Math. 56 (1998), 553-568
MSC: Primary 76B47
DOI: https://doi.org/10.1090/qam/1632318
MathSciNet review: MR1632318
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Given a stable configuration of point vortices for steady two-dimensional inviscid, incompressible fluid flow in a domain $D$, it is shown that there is another stable configuration of stationary vortices in $D$ with vortices near the original vortices plus additional vortices near any points on the boundary where the speed of the original flow is a nonzero relative minimum.

M. S. Berger and L. E. Fraenkel, Nonlinear desingularization in certain free-boundary problems, Comm. Math. Phys. 77 (1980), no. 2, 149–172. MR 589430
A. R. Elcrat, C. Hu, and K. G. Miller, Equilibrium configurations of point vortices for channel flows past interior obstacles, European J. Mech. B Fluids 16 (1997), no. 2, 277–292. MR 1439068
Alan R. Elcrat and Kenneth G. Miller, Rearrangements in steady multiple vortex flows, Comm. Partial Differential Equations 20 (1995), no. 9-10, 1481–1490. MR 1349221, DOI https://doi.org/10.1080/03605309508821141

B. Gustafsson, On the motion of a vortex in two-dimensional flow of an ideal fluid in simply and multiply connected domains, Research Report, Dept. of Mathematics, Royal Institute of Technology, Stockholm, 1979

M. K. Huang and C. Y. Chow, Trapping a free vortex by Joukowski airfoils, AIAA Journal 20, 292–298 (1982)

C. C. Lin, On the Motion of Vortices in Two Dimensions, University of Toronto Studies, Applied Mathematics Series, no. 5, University of Toronto Press, Toronto, Ont., 1943. MR 0008204
Kenneth G. Miller, Stationary corner vortex configurations, Z. Angew. Math. Phys. 47 (1996), no. 1, 39–56. MR 1408670, DOI https://doi.org/10.1007/BF00917573
P. G. Saffman, Vortex dynamics, Cambridge Monographs on Mechanics and Applied Mathematics, Cambridge University Press, New York, 1992. MR 1217252
P. G. Saffman and J. S. Scheffield, Flow over a wing with an attached free vortex, Studies in Appl. Math. 57 (1976/77), no. 2, 107–117. MR 462150, DOI https://doi.org/10.1002/sapm1977572107
Bruce Turkington, On steady vortex flow in two dimensions. I, II, Comm. Partial Differential Equations 8 (1983), no. 9, 999–1030, 1031–1071. MR 702729, DOI https://doi.org/10.1080/03605308308820293
Bruce Turkington and Alexander Eydeland, An iterative method for computing steady vortex flow systems, Mathematical aspects of vortex dynamics (Leesburg, VA, 1988) SIAM, Philadelphia, PA, 1989, pp. 80–87. MR 1001791
Yieh Hei Wan, Desingularizations of systems of point vortices, Phys. D 32 (1988), no. 2, 277–295. MR 969034, DOI https://doi.org/10.1016/0167-2789%2888%2990056-5