Islands in three-dimensional steady flows

C. C. Hegna, A. Bhattacharjee

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We consider the problem of steady Euler flows in a torus. We show that in the absence of a direction of symmetry the solution for the vorticity contains δ-function singularities at the rational surfaces of the torus. We study the effect of a small but finite viscosity on these singularities. The solutions near a rational surface contain cat’s eyes or islands, well known in the classical theory of critical layers. When the islands are small, their widths can be computed by a boundary-layer analysis. We show that the islands at neighbouring rational surfaces generally overlap. Thus, steady toroidal flows exhibit a tendency towards Beltramization.

Original languageEnglish (US)
Pages (from-to)527-542
Number of pages16
JournalJournal of Fluid Mechanics
StatePublished - Jun 1991
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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