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Helical vortices: Quasiequilibrium states and their time evolution

Can Selçuk

Ivan Delbende*

Maurice Rossi

  • LIMSI, CNRS, Université Paris–Saclay, Rue John von Neumann, 91405 Orsay, France and IFD, UPMC, Sorbonne Universités, 4 place Jussieu, 75005 Paris, France

  • UFR d'Ingénierie, UPMC, Sorbonne Universités, 4 place Jussieu, 75005 Paris, France and LIMSI, CNRS, Université Paris–Saclay, Rue John von Neumann, 91405 Orsay, France

  • CNRS, UMR No. 7190, Institut Jean Le Rond d'Alembert, 75005 Paris, France and UPMC, Sorbonne Universités, UMR No. 7190, Institut Jean Le Rond d'Alembert, 75005 Paris, France

  • *Corresponding author: Ivan.Delbende@limsi.fr
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Phys. Rev. Fluids 2, 084701 – Published 15 August, 2017

DOI: https://doi.org/10.1103/PhysRevFluids.2.084701

Abstract

The time evolution of a viscous helical vortex is investigated by direct numerical simulations of the Navier-Stokes equations where helical symmetry is enforced. Using conservation laws in the framework of helical symmetry, we elaborate an initial condition consisting in a finite core vortex, the time evolution of which leads to a generic quasiequilibrium state independent of the initial core size. Numerical results at different helical pitch values provide an accurate characterization in time for such helical states, for which specific techniques have been introduced: helix radius, angular velocity, stream function–velocity–vorticity relationships, and core properties (size, self-similarity, and ellipticity). Viscosity is shown to be at the origin of a small helical velocity component, which we relate to the helical vorticity component. Finally, changes in time of the flow topology are studied using the helical stream function and three-dimensional Lagrangian orbits.

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References (36)

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Phys. Rev. Fluids 2, 084701– Published 15 August, 2017
  • Received 3 January 2017

©2017 American Physical Society

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