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Interacting vorticity waves as an instability mechanism for magnetohydrodynamic shear instabilities

Published online by Cambridge University Press:  12 February 2015

E. Heifetz ,
J. Mak ,
J. Nycander  and
O. M. Umurhan
E. Heifetz
Affiliation:
Department of Geophysics and Planetary Sciences, Tel Aviv University, Tel Aviv, 69978, Israel Department of Meteorology (MISU), Stockholm University, SE-106 91 Stockholm, Sweden
J. Mak
Affiliation:
Department of Geophysics and Planetary Sciences, Tel Aviv University, Tel Aviv, 69978, Israel
J. Nycander
Affiliation:
Department of Meteorology (MISU), Stockholm University, SE-106 91 Stockholm, Sweden
O. M. Umurhan
Affiliation:
NASA Ames Research, Space Sciences Division, Mail Stop N-245-3, Moffett Field, CA 94043, USA SETI Institute, 189 Bernardo Avenue, Suite 100, Mountain View, CA 94043, USA
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Abstract

The interacting vorticity wave formalism for shear flow instabilities is extended here to the magnetohydrodynamic (MHD) setting, to provide a mechanistic description for stabilising and destabilising shear instabilities by the presence of a background magnetic field. The interpretation relies on local vorticity anomalies inducing a non-local velocity field, resulting in action at a distance. It is shown here that the waves supported by the system are able to propagate vorticity via the Lorentz force, and waves may interact. The existence of instability then rests upon whether the choice of basic state allows for phase locking and constructive interference of the vorticity waves via mutual interaction. To substantiate this claim, we solve the instability problem of two representative basic states, one where a background magnetic field stabilises an unstable flow and the other where the field destabilises a stable flow, and perform relevant analyses to show how this mechanism operates in MHD.

JFM classification

Instability: Instability MHD and Electrohydrodynamics: Magnetic fluids MHD and Electrohydrodynamics: MHD and Electrohydrodynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 767 , 25 March 2015 , pp. 199 - 225
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Copyright
© 2015 Cambridge University Press 

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