Short-wave stability of a helical vortex tube: the effect of torsion on the curvature instability

Abstract

In this paper, we study the short-wave stability of a helical vortex tube. The base flow field inside the helical vortex tube is obtained by perturbation expansion assuming that ${\epsilon}$, the ratio of the core to curvature radius of the helical tube, be small. After reviewing our recent results obtained by the short-wavelength stability analysis, the normal-mode stability analysis is carried out to confirm the results and pursue further details. It is shown that the helical vortex tube suffers from curvature instability found for vortex rings. The growth rate of the curvature instability is obtained both analytically and numerically. The effect of torsion and rotation on the stability appears at the second order of ${\epsilon}$. It is shown that the effects of rotation on the growth rate found by normal-mode stability analysis converges to those found by short-wavelength stability analysis in the short-wave limit.