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Effects of magnetic field on the turbulent wake of a cylinder in free-surface magnetohydrodynamic channel flow

Published online by Cambridge University Press:  25 February 2014

John R. Rhoads ,
Eric M. Edlund  and
Hantao Ji
John R. Rhoads*
Affiliation:
Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544, USA
Eric M. Edlund
Affiliation:
Princeton Plasma Physics Laboratory, Princeton, NJ 08543, USA
Hantao Ji
Affiliation:
Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544, USA Princeton Plasma Physics Laboratory, Princeton, NJ 08543, USA
*
†Email address for correspondence: jrhoads@pppl.gov
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Abstract

Results from a free-surface magnetohydrodynamic (MHD) flow experiment are presented detailing the modification of vortices in the wake of a circular cylinder with its axis parallel to the applied magnetic field. Experiments were performed at Reynolds numbers of the order of ${\mathit{Re}}\sim 10^4$ as the interaction parameter ${\mathit{N}}$, representing the ratio of electromagnetic forces to inertial forces, was increased through unity. The von Kármán vortex street in the wake of the cylinder was observed by simultaneously sampling the gradient of the induced electric potential, $ \boldsymbol {\nabla }{\phi }$, at 16 cross-stream locations as a proxy for the streamwise fluid velocity. An ensemble of vortex velocity profiles was measured as a function of the applied magnetic field strength. Results indicate a significant change in the circulation of vortices and the deviations from the average profile as ${\mathit{N}}$ was increased. By sampling the fluctuations in $\boldsymbol {\nabla }{\phi }$ at three locations in the wake, the decay of the vortices was examined and the effective viscosity was found to decrease as ${\mathit{N}}^{-0.49 \pm 0.04}$. Using temperature as a passive tracer, qualitative observations were made with an infrared (IR) camera that showed significant changes in the wake, including the absence of small-scale structures at high magnetic field strengths. Collectively, the results suggest that the reduction in effective viscosity was due to the suppression of the small-scale eddies by the magnetic field. The slope of the power spectrum was observed to change from a $k^{-1.8}$ power law at low ${\mathit{N}}$ to a $k^{-3.5}$ power law for ${\mathit{N}}> 1$. Together, these results suggest the flow smoothly transitioned from a hydrodynamic state to a magnetohydrodynamic regime over the range of $0 < {\mathit{N}}< 1$.

JFM classification

MHD and Electrohydrodynamics: MHD and Electrohydrodynamics MHD and Electrohydrodynamics: MHD turbulence Vortex Flows: Vortex dynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 742 , 10 March 2014 , pp. 446 - 465
Copyright
© 2014 Cambridge University Press 

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Rhoads et al. supplementary movie

Compilation of infrared movies showing the qualitative behavior of vortices in the wake of a cylinder as the interaction parameter, N, is increased.

Download Rhoads et al. supplementary movie(Video)
Video 9.6 MB