ON THE EXISTENCE OF STEADY HELICAL VORTEX TUBES OF SMALL CROSS-SECTION
- 1 May 1981
- journal article
- research article
- Published by Oxford University Press (OUP) in The Quarterly Journal of Mechanics and Applied Mathematics
- Vol. 34 (2) , 153-177
- https://doi.org/10.1093/qjmam/34.2.153
Abstract
This paper is concerned with proving the existence of steady helical vortex tubes of small cross-section in fluid which is inviscid, incompressible, and of uniform density. A stream function is introduced and the problem is reduced to proving the existence of a solution of a certain nonlinear integral equation. The equation is decomposed into linear and nonlinear terms and the existence of a solution is established with the aid of a theorem in the paper by Fraenkel (1) on steady vortex rings of small cross-section. The first approximations to the propagation speed, circulation and cross-sectional area are obtained.Keywords
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