Global organization of three-dimensional, volume-preserving flows: constraints, degenerate points, and Lagrangian structure

Bharath Ravu, Guy Metcalfe, Murray Rudman, Daniel R. Lester, Devang V. Khakhar

Research output: Contribution to journalArticleResearchpeer-review


Global organization of three-dimensional (3D) Lagrangian chaotic transport is difficult to infer without extensive computation. For 3D time-periodic flows with one invariant, we show how constraints on deformation that arise from volume-preservation and periodic lines result in resonant degenerate points that periodically have zero net deformation. These points organize all Lagrangian transport in such flows through coordination of lower-order and higher-order periodic lines and prefigure unique transport structures that arise after perturbation and breaking of the invariant. Degenerate points of periodic lines and the extended 3D structures associated with them are easily identified through the trace of the deformation tensor calculated along periodic lines. These results reveal the importance of degenerate points in understanding transport in one-invariant fluid flows.

Original languageEnglish
Article number033124
Number of pages23
Issue number3
Publication statusPublished - Mar 2020

Cite this