The Godbillon-Vey invariant as topological vorticity compression and obstruction to steady flow in ideal fluids

Research output: Contribution to journalArticle (Academic Journal)peer-review

Abstract

If the vorticity field of an ideal fluid is tangent to a foliation, additional conservation laws arise. For a class of zero-helicity vorticity fields, the Godbillon-Vey (GV) invariant of foliations is defined and is shown to be an invariant purely of the vorticity, becoming a higher-order helicity-type invariant of the flow. GV ≠ 0 gives both a global topological obstruction to steady flow and, in a particular form, a local obstruction. GV is interpreted as helical compression and stretching of vortex lines. Examples are given where the value of GV is determined by a set of distinguished closed vortex lines.
Original languageEnglish
JournalProceedings of the Royal Society A: Mathematical and Physical Sciences
Volume476
Issue number20190851
DOIs
Publication statusPublished - 8 Jul 2020

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