# Lamb-Chaplygin dipole

There is an interesting issue of hydrodynamics: whirlpools.

I want to learn about the Lamb-Chaplygin dipole.

Lamb-Chaplygin dipole corresponds to a steady solution of the two dimensional Euler equations.

Can someone know where I can find a full development of Lamb-Chaplygin dipole?

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## 1 Answer

The following is relevant: V.V. Meleshko and G.J.F. van Heijst, "On Chaplygin's investigations of two-dimensional vortex structures in an inviscid fluid," J. Fluid Mech. 272, 157-182, 1994 . While their outline may be less than "full", their bibliography looks comprehensive.

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thank you, I just want to be sure. the solution is found in this document? ics.org.ru/doc?pdf=875&dir=e –  Alon Shmiel Jan 27 '13 at 22:42
Looks like that. –  akhmeteli Jan 27 '13 at 23:28
thank you very much! is the answer found in all of the pages (220-230) or just between 220 to 226? –  Alon Shmiel Jan 28 '13 at 7:55
I believe the answer is at pp. 219-225. The following commentary seems to add some details for the case of circular vortex motion, although this case is also handled in Chaplygin's paper, although briefly. –  akhmeteli Jan 28 '13 at 13:21
thanks! you help me so much! –  Alon Shmiel Jan 28 '13 at 13:34