Numerical Analysis Seminars: How to (un)braid a magnetic field
17 February 2012 14:00 in CG83
Magnetic fields as well as vorticity field or other divergence-free fields often show knotted or linked field lines. Knottedness or linkage are topological invariants and a natural question is whether we can quantify these properties for divergence-free vector fields. We show how this is done for the simplest form of linkage, the Gaussian linkage, and how this leads to a very robust invariant, the magnetic helicity. We give a short overview of the properties of the helicity integral, how it evolves under dissipation, and discuss the possibility of finding similar integrals which measure other (higher-order) types of linking. We then present some recent results regarding the turbulent relaxation of braided magnetic fields which demonstrate the relevance of invariants that go beyond magnetic helicity.
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