Helicity in axisymmetric vortex breakdown

TL;DR

This paper investigates the role of helicity in axisymmetric vortex breakdown, proposing a simplified model that links negative helicity to vortex breakdown phenomena in geophysical and engineering flows.

Contribution

It introduces a simplified formulation of helicity in vortex breakdown and demonstrates its effectiveness in identifying and characterizing vortex breakdowns.

Findings

Negative helicity correlates with vortex breakdown.

Helicity density governs vortex topology.

Model verifies the helicity-based characterization.

Abstract

Vortex breakdown phenomena in the axial vortices is an important feature which occurs frequently in geophysical flows (tornadoes and hurricanes) and in engineering flows (flow past delta wings, Von-Kerman vortex dynamo). We analyze helicity for axisymmetric vortex breakdown and propose a simplified formulation. For such cases, negative helicity is shown to conform to the vortex breakdown. A model problem has been analyzed to verify the results. The topology of the vortex breakdown is governed entirely by helicity density in the vertical plane. Our proposed methodology may be regarded as the prototype for identifying and characterize the breakdowns/eye in more complicated large-scale flows such as tornadoes/hurricanes.