Equilibrium vortex configurations in domains with boundary
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
M. S. Berger and L. E. Fraenkel, Nonlinear desingularization in certain free-boundary problems, Commun. Math. Phys. 77, 149–172 (1980)
A. R. Elcrat, C. Hu, and K. G. Miller, Equilibrium configurations of point vortices for channel flow past interior obstacles, European J. Mech. B Fluids 16, 277–292 (1997)
A. R. Elcrat and K. G. Miller, Rearrangements in steady multiple vortex flows, Comm. Partial Differential Equations 20, 1481–1490 (1995)
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, Univ. Toronto Appl. Math. Series, no. 5, Toronto Univ. Press, 1943
K. G. Miller, Stationary corner vortex configurations, Z. angew. Math. Phys. 47, 39–56 (1996)
P. G. Saffman, Vortex Dynamics, Cambridge University Press, Cambridge, 1992
P. G. Saffman and J. Sheffield, Flow over a wing with an attached free vortex, Studies in Applied Math. 57, 107–117 (1977)
B. Turkington, On steady vortex flow in two dimensions, I, Comm. Partial Differential Equations 8, 999–1030 (1983)
B. Turkington and A. Eydeland, An iterative method for computing steady vortex flow systems, Proceedings of the Workshop on Mathematical Aspects of Vortex Dynamics (R. Caflisch, ed.), SIAM, Philadelphia, 1989, pp. 80–87
Y. H. Wan, Desingularization of systems of point vortices, Phys. D 32, 277–295 (1988)
Similar Articles
Retrieve articles in Quarterly of Applied Mathematics
with MSC:
76B47
Retrieve articles in all journals
with MSC:
76B47
Additional Information
Article copyright:
© Copyright 1998
American Mathematical Society