Instability of a Helical Vortex Tube with Axial Flow

• Hattori Yuji

  Institute of Fluid Science, Tohoku University

• Fukumoto Yasuhide

  Institute of Mathematics for Industry, Kyushu University

Bibliographic Information

Other Title

• 軸流をもつらせん渦の不安定性

Abstract

The stability of a helical vortex tube with axial flow is studied analytically. The base flow is obtained by solving the Euler equation perturbatively assuming small ratio of core to curvature radius, which is denoted by \epsilon, and Rankine vortex with uniform axial flow at the leading order. We apply both local and modal stability analysis. By local stability analysis we show that the flow is subject to not only curvature instability but also Coriolis instability, both having the same resonance condition. The unstable growth rate is O(\epsilon) and given by the magnitude of a sum of the complex numbers corresponding to the two instabilities. Combined effects of the axial flow and the torsion of the helical vortex tube appear as O(\epsilon^2) modification. These results are confirmed by the modal stability analysis.

Journal

• NCTAM papers, National Congress of Theoretical and Applied Mechanics, Japan

  NCTAM papers, National Congress of Theoretical and Applied Mechanics, Japan 61 (0), 39-39, 2012

  National Committee for IUTAM

Keywords

• helical vortex
• local stability analysis
• modal stability analysis
• curvature instability
• axial flow

Details

• CRID: 1390282680570243456
• NII Article ID: 130005020750
• DOI: 10.11345/japannctam.61.0.39.0
• Text Lang: ja
• Data Source:
  • JaLC
  • CiNii Articles
• Abstract License Flag: Disallowed