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Updated: Sep 24, 2025

Preparation of Free-Surface Hyperbolic Water Vortices
Published on: July 28, 2023
Equations of motion for weakly compressible point vortices
Stefan G Llewellyn Smith1,2, T Chu1, Z Hu3
1Department of Mechanical and Aerospace Engineering, Jacobs School of Engineering, UCSD, 9500 Gilman Drive, La Jolla, CA 92093-0411, USA.
Abstract:
Equations of motion for compressible point vortices in the plane are obtained in the limit of small Mach number, M, using a Rayleigh-Jansen expansion and the method of Matched Asymptotic Expansions. The solution in the region between vortices is matched to solutions around each vortex core. The motion of the vortices is modified over long time scales [Formula: see text] and [Formula: see text]. Examples are given for co-rotating and co-propagating vortex pairs. The former show a correction to the rotation rate and, in general, to the centre and radius of rotation, while the latter recover the known result that the steady propagation velocity is unchanged. For unsteady configurations, the vortex solution matches to a far field in which acoustic waves are radiated. This article is part of the theme issue 'Mathematical problems in physical fluid dynamics (part 2)'.
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