A family of exact solutions of the Euler equations is presented: they are generalizations of the Kirchhoff vortex to N confocal ellipses. Special attention is given to the case N=2, for which the stability is analyzed with a method similar to the one used by Love [Proc. London Math. Soc. 1, XXV 18 (1893)] for the Kirchhoff vortex. The results are compared with those for the corresponding circular problem.

1.
H. Lamb, Hydrodynamics, 6th ed. (Dover, New York, 1932).
2.
A. E. H.
Love
,
Proc. London Math. Soc.
1
,
XXV
 
18
(
1893
).
3.
See National Technical Information Service Document No. AD‐A149386/5 (Woods Hole Oceanographic Institution Technical Report, WHOI‐84‐44). Copies may be ordered from the National Technical Information Service, Springfield, Virginia, 22161. The price is $22.95 plus a $3.00 handling fee. All orders must be prepaid.
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© 1986 American Institute of Physics.
1986
American Institute of Physics
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