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Lissajous trajectories in electromagnetically driven vortices

Published online by Cambridge University Press:  21 February 2017

Aldo Figueroa Open the ORCID record for Aldo Figueroa [Opens in a new window] ,
Sergio Cuevas  and
Eduardo Ramos
Aldo Figueroa*
Affiliation:
CONACYT-Centro de Investigación en Ciencias, Universidad Autónoma del Estado de Morelos, Cuernavaca, Mor. 62209, México
Sergio Cuevas
Affiliation:
Instituto Energías Renovables, Universidad Nacional Autónoma de México, AP 34, Temixco, Mor. 62580, México
Eduardo Ramos
Affiliation:
Instituto Energías Renovables, Universidad Nacional Autónoma de México, AP 34, Temixco, Mor. 62580, México
*
†Email address for correspondence: alfil@uaem.mx
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Abstract

An experimental and theoretical study of laminar vortical flows driven by oscillating electromagnetic forces that act in orthogonal directions in a shallow electrolytic fluid layer is presented. Forces are generated by the interaction of the field of a dipolar permanent magnet and two imposed alternating electric currents perpendicular to each other with independent frequencies varying in the range of 10–30 mHz. Velocity fields of the time-dependent flow are obtained using particle image velocimetry, while particle tracking allows exploration of the Lagrangian trajectories and time maps. An approximate two-dimensional analytical solution is obtained for the laminar creeping regime so that Lagrangian trajectories are integrated explicitly. These trajectories resemble Lissajous figures with the usual property that, when the ratio of the frequencies of the imposed currents is rational, closed paths are found, while non-closed paths occur when this ratio is irrational. Deviations of this regime that account for slight increase of inertial effects are explored through a quasi-two-dimensional numerical simulation. In this case, non-closed paths are found even for rational frequency ratios. This case was observed in the experiment. Lagrangian trajectories calculated numerically show a qualitative agreement with experimental particle tracking. Furthermore, numerical time maps obtained for increasing inertial effects and rational frequency ratios reveal a chaotic behaviour. Some features of the Lagrangian trajectories are validated experimentally. In particular, topological properties of the calculated and observed time maps are in qualitative agreement. In a characteristic case, a partial time map calculated numerically is compared with the section acquired from the experimental tracking of one particle.

JFM classification

Mixing: Chaotic advection Vortex Flows: Vortex dynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 815 , 25 March 2017 , pp. 415 - 434
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Copyright
© 2017 Cambridge University Press 

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