Knot spectrum of turbulence

Streamlines, vortex lines and magnetic flux tubes in turbulent fluids and plasmas display a great amount of coiling, twisting and linking, raising the question as to whether their topological complexity (continually created and destroyed by reconnections) can be quantified. In superfluid helium, the...

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Bibliographic Details
Published in:arXiv.org 2019-07
Main Authors: Cooper, R G, Mesgarnezhad, M, Baggaley, A W, Barenghi, C F
Format: Article
Language:English
Subjects:
Coiling
Computational fluid dynamics
Computer simulation
Fluid flow
Fluids
Helium
Knots
Macromolecules
Magnetic flux
Plasmas
Polynomials
Quantum turbulence
Reforming
Scaling laws
Superfluidity
Topology
Tubes
Twisting
Vortices
Vorticity
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Summary:Streamlines, vortex lines and magnetic flux tubes in turbulent fluids and plasmas display a great amount of coiling, twisting and linking, raising the question as to whether their topological complexity (continually created and destroyed by reconnections) can be quantified. In superfluid helium, the discrete (quantized) nature of vorticity can be exploited to associate to each vortex loop a knot invariant called the Alexander polynomial whose degree characterizes the topology of that vortex loop. By numerically simulating the dynamics of a tangle of quantum vortex lines, we find that this quantum turbulence always contains vortex knots of very large degree which keep forming, vanishing and reforming, creating a distribution of topologies which we quantify in terms of a knot spectrum and its scaling law. We also find results analogous to those in the wider literature, demonstrating that the knotting probability of the vortex tangle grows with the vortex length, as for macromolecules, and saturates above a characteristic length, as found for tumbled strings.
ISSN:2331-8422