Planar Limits of Three-Dimensional Incompressible Flows with Helical Symmetry

Milton C. Lopes Filho, Anna L. Mazzucato, Dongjuan Niu, Helena J. Nussenzveig Lopes, Edriss S. Titi

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7 Scopus citations


Helical symmetry is invariance under a one-dimensional group of rigid motions generated by a simultaneous rotation around a fixed axis and translation along the same axis. The key parameter in helical symmetry is the step or pitch, the magnitude of the translation after rotating one full turn around the symmetry axis. In this article we study the limits of three-dimensional helical viscous and inviscid incompressible flows in an infinite circular pipe, with respectively no-slip and no-penetration boundary conditions, as the step approaches infinity. We show that, as the step becomes large, the three-dimensional helical flow approaches a planar flow, which is governed by the so-called two-and-half Navier–Stokes and Euler equations, respectively.

Original languageEnglish (US)
Pages (from-to)843-869
Number of pages27
JournalJournal of Dynamics and Differential Equations
Issue number4
StatePublished - Dec 9 2014

All Science Journal Classification (ASJC) codes

  • Analysis


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