Effects of axial flow on the stability of a helical vortex tube

• Published in: Physics of fluids (1994) 2012-05, Vol.24 (5), p.054102-054102-15
• Main Authors: Hattori, Y., Fukumoto, Y.
• Format: Article
• Language: English
• Subjects: Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); Hydrodynamic stability; Inviscid flows with vorticity; Inviscid instability; Laminar flows; Physics
• ISSN: 1070-6631; 1089-7666
• DOI: 10.1063/1.4717769

The effects of axial flow on the stability of a helical vortex tube are studied by short-wavelength stability analysis. By axial flow we mean the flow along the helical tube inside the vortex core. At the leading order the base flow is set to the Rankine vortex with uniform velocity along the helical tube. The exponential growth rate is obtained analytically as the magnitude of the sum of three O(ε) and five O(ε2) complex numbers, where ε is the ratio of the core to curvature radius. At O(ε) the effect of axial flow can be regarded as the effect of the Coriolis force; as a result the instability is the superposition of the curvature instability and the Coriolis or precessional instability since the two instabilities occur under the same resonance condition. At O(ε2) combined effects of the axial flow and the torsion appear; the maximum growth rate increases when the period of particle motion increases.