Abstract
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 language | English (US) |
|---|---|
| Pages (from-to) | 843-869 |
| Number of pages | 27 |
| Journal | Journal of Dynamics and Differential Equations |
| Volume | 26 |
| Issue number | 4 |
| DOIs | |
| State | Published - Dec 9 2014 |
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All Science Journal Classification (ASJC) codes
- Analysis
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Planar Limits of Three-Dimensional Incompressible Flows with Helical Symmetry. / Lopes Filho, Milton C.; Mazzucato, Anna L.; Niu, Dongjuan; Nussenzveig Lopes, Helena J.; Titi, Edriss S.
In: Journal of Dynamics and Differential Equations, Vol. 26, No. 4, 09.12.2014, p. 843-869.Research output: Contribution to journal › Article
TY - JOUR
T1 - Planar Limits of Three-Dimensional Incompressible Flows with Helical Symmetry
AU - Lopes Filho, Milton C.
AU - Mazzucato, Anna L.
AU - Niu, Dongjuan
AU - Nussenzveig Lopes, Helena J.
AU - Titi, Edriss S.
PY - 2014/12/9
Y1 - 2014/12/9
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84916886708&partnerID=8YFLogxK
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U2 - 10.1007/s10884-014-9411-0
DO - 10.1007/s10884-014-9411-0
M3 - Article
AN - SCOPUS:84916886708
VL - 26
SP - 843
EP - 869
JO - Journal of Dynamics and Differential Equations
JF - Journal of Dynamics and Differential Equations
SN - 1040-7294
IS - 4
ER -