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The Quarterly Journal of Mechanics and Applied Mathematics 2001 54(2):243-256; doi:10.1093/qjmam/54.2.243
© 2001 by Oxford University Press
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Flow of an Inviscid Rotating Liquid into an Elevated Sink

Alan Shapiro1

( 1 School of Meteorology, University of Oklahoma, Norman, Oklahoma 73019, USA )

Long's solution (Q. Jl Mech. Appl. Math. 9 (1956) 385–393) for steady flow of a rotating liquid into a hydrodynamic sink at the base of a cylinder is extended to the case where the sink is elevated above the cylinder base. The solution satisfies the nonlinear Euler equations exactly for all sink heights and for swirl ratios (inverse Rossby numbers) less than a finite critical value. Flow above the elevated sink is qualitatively similar to that in Long's original solution, while flow beneath the sink is comprised of a very weak meridional circulation and an intense nearly-potential vortex.


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