Planar Limits of Three-Dimensional Incompressible Flows with Helical Symmetry uri icon

abstract

  • 2014, Springer Science+Business Media New York. 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 NavierStokes and Euler equations, respectively.

published proceedings

  • JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS

altmetric score

  • 0.25

author list (cited authors)

  • Lopes Filho, M. C., Mazzucato, A. L., Niu, D., Nussenzveig Lopes, H. J., & Titi, E. S.

citation count

  • 7

complete list of authors

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

publication date

  • December 2014