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Entanglement transitions in one-dimensional confined fluid flows

The strength of entanglement present in a tubular structure consisting of short filaments is assessed using a periodic boundary condition model by employing the magnitude of the eigenvalues of the periodic linking matrix associated to the filamental structure. The effects of tube radius and of the alignment of the filaments on the strength of entanglement are shown to suggest that strongly aligned flow systems exhibit a stronger entanglement than those consisting of randomly aligned filaments of the same density. Our results could be used to quantify the entanglement of vortex filaments and understand the effects of vortex filament alignment in fluid flows.