Variety of unsymmetric multibranched logarithmic vortex spirals
2017 ◽
Vol 30
(1)
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pp. 23-38
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Keyword(s):
Building on work of Prandtl and Alexander, we study logarithmic vortex spiral solutions of the two-dimensional incompressible Euler equations. We consider multi-branched spirals that are not symmetric, including mixtures of sheets and continuum vorticity. We find that non-trivial solutions allow only sheets, that there is a large variety of such solutions, but that only the Alexander spirals with three or more symmetric branches appear to yield convergent Biot–Savart integral.
1988 ◽
Vol 79
(1)
◽
pp. 70-84
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2015 ◽
pp. 135-155
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2019 ◽
Vol 20
(5)
◽
pp. 1309-1362
2018 ◽
Vol 79
(2)
◽
pp. 1111-1134
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2017 ◽
Vol 73
(2-3)
◽
pp. 1316-1337
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1999 ◽
Vol 37
(6)
◽
pp. 1874-1896
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2005 ◽
Vol 25
(3)
◽
pp. 507-522
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Keyword(s):