Curvature and elliptic instabilities in helical vortices (INVITED)

Abstract eng:
Short-wavelength instabilities of helical vortices are analysed using a combined theoretical and numerical approach. The helical vortices are described using an asymptotic approach in the limit of small core size (compared to the pitch and the radius of the helix). Both the curvature instability induced by the local vortex curvature and the elliptic instability induced by the strain field deformation are considered for a vortex with Gaussian axial vorticity and axial velocity (Batchelor vortex). Theoretical predictions are obtained for the growth rate of each instability and used to analyse the competition between both instabilities. We show the crucial role of the axial flow component of the Batchelor vortex in the selection of the dominant instability. For weak axial flow, the elliptic instability is found to dominate the curvature instability, whereas it is the opposite when the axial flow is no longer negligible. The results are compared to recent experimental observations.

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