Topology and transport in generalized helical flows

Abstract

Pure helical or screw flow presents a unique combination of zero net advection, alignment of vorticity dissipation with vorticity field, and maximal helicity. Helicity is a measure of knottedness in a flow structure as manifested in terms of a net imbalance between right and left handed helical motion. Topology, which is intrinsic to helicity, provides a geometric perspective to vortex reconnection in helical flow. However, the topological evolution and the resulting transport in helical flows remain unclear. Here, we investigate the evolution of isosurfaces associated with the Galilean invariant Q-criterion in generalized models of helical flow. While we categorize the stagnation points with Δ-criterion, the Gaussian curvature shows that the creation and annihilation of these points occur in pairs for specific instances of helical flow. The contours of finite-time Lyapunov exponent reveal the fluidic mixing due to the strain and shear transport barriers. These findings have far-reaching implications in diverse fields, ranging from classical turbulence in superfluid helium to dynamos in growing magnetic field. The present article sheds insights into these applications.