Thin helical vortex dynamics in low-viscosity liquid

Abstract

The problem of helical vortices description has the significant interest as from fundamental point of view as well for practice. In some sense this problem is close to the vortex ring one which attracted much more attention in last decades. The reviews on the vortex rings investigations can be found in recent papers (1, 2) or in book by Akhmetov (3). In particular, in series of papers by Kaplanskii with co-authors (4-6) there was considered the viscosity influence on the vortex ring evolution. Separate attention was paid to the low Reynolds number case and to high Reynolds number one, initial stage of viscous evolution and final one. This paper presents first attempt for research on the diffusion and dynamics of a viscous helical vortex. In this work the problem of thin helical dynamics in low-viscosity liquid is considered. Appearance of helical vortex in the flow assumes helical symmetry. It means, that all of flow characteristic will be constant along the helical lines. The flow of viscous incompressible fluid under condition of the helical symmetry is described in variables vorticity - stream function by the system of equations (7, 8) 2