Optimal unstirred state of a passive scalar

L. Chen, A. R. Yeates (Lead / Corresponding author), A. B. J. Russell

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1 Citation (Scopus)
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Given a passive tracer distribution, what is the simplest unstirred pattern that may be reached under incompressible advection? This question is partially motivated by recent studies of three-dimensional (3-D) magnetic reconnection, in which the patterns of a topological invariant called the field line helicity greatly simplify until reaching a relaxed state. We test two approaches: a variational method with minimal constraints, and a magnetic relaxation scheme where the velocity is determined explicitly by the pattern of. Both methods achieve similar convergence for simple test cases. However, the magnetic relaxation method guarantees a monotonic decrease in the Dirichlet seminorm of, and is numerically more robust. We therefore apply the latter method to two complex mixed patterns modelled on the field line helicity of 3-D magnetic braids. The unstirring separates into a small number of large-scale regions determined by the initial topology, which is well preserved during the computation. Interestingly, the velocity field is found to have the same large-scale topology as. Similarity to the simplification found empirically in 3-D magnetic reconnection simulations supports the idea that advection is an important principle for field line helicity evolution.

Original languageEnglish
Article numberA30
Number of pages21
JournalJournal of Fluid Mechanics
Early online date28 Jan 2021
Publication statusPublished - 25 Mar 2021


  • Key words variational methods
  • topological fluid dynamics

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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