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Hollow vortex in a corner

Published online by Cambridge University Press:  07 December 2020

T. W. Christopher Open the ORCID record for T. W. Christopher [Opens in a new window]  and
Stefan G. Llewellyn Smith Open the ORCID record for Stefan G. Llewellyn Smith [Opens in a new window]
T. W. Christopher*
Affiliation:
Department of Mechanical and Aerospace Engineering, Jacobs School of Engineering, UCSD, 9500 Gilman Drive, La Jolla, CA92093-0411, USA
Stefan G. Llewellyn Smith
Affiliation:
Department of Mechanical and Aerospace Engineering, Jacobs School of Engineering, UCSD, 9500 Gilman Drive, La Jolla, CA92093-0411, USA Scripps Institution of Oceanography, UCSD, 9500 Gilman Drive, La Jolla, CA92093-0230, USA
*
†Email address for correspondence: [email protected]
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Abstract

Equilibrium solutions for hollow vortices in straining flow in a corner are obtained by solving a free-boundary problem. Conformal maps from a canonical doubly connected annular domain to the physical plane combining the Schottky–Klein prime function with an appropriate algebraic map lead to a problem similar to Pocklington's propagating hollow dipole. The result is a two-parameter family of solutions depending on the corner angle and on the non-dimensional ratio of strain to circulation.

JFM classification

Vortex Flows: Vortex dynamics
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 908 , 10 February 2021 , R2
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

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