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BeijingMoscow Mathematics Colloquium
June 26, 2020 15:00–16:00, Moscow, online
 


Tying Knots in Fluids

Yu. Yang

Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing

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Abstract: We develop a general method for constructing knotted vortex/magnetic tubes with the finite thickness, arbitrary shape, and tunable twist. The central axis of the knotted tubes is determined by a given smooth and non-degenerated parametric equation. The helicity of the knotted tubes can be explicitly decomposed into the writhe, localized torsion, and intrinsic twist. We construct several knotted vortex/magnetic tubes with various geometry and topology, and investigate the effect of twist on their evolution in hydrodynamic or magnetohydrodynamic flows using direct numerical simulation. In addition, we illustrate a knot cascade of magnetic field lines through the stepwise reconnection of a pair of orthogonal helical flux tubes with opposite chirality.

Language: English

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