VIOLATION OF RICHARDSON'S CRITERION VIA INTRODUCTION OF A MAGNETIC FIELD
- Department of Physics, University of Wisconsin, Madison, WI 53706 (United States)
- Departments of Astronomy and Physics, University of Wisconsin, Madison, WI 53706 (United States)
- Department of Astronomy, University of Wisconsin, Madison, WI 53706 (United States)
Shear flow instabilities can profoundly affect the diffusion of momentum in jets, stars, and disks. The Richardson criterion gives a sufficient condition for instability of a shear flow in a stratified medium. The velocity gradient V' can only destabilize a stably stratified medium with squared Brunt-Vaeisaelae frequency N {sup 2} if V'{sup 2}/4>N {sup 2}. We find this is no longer true when the medium is a magnetized plasma. We investigate the effect of stable stratification on the magnetic field and velocity profiles unstable to magneto-shear instabilities, i.e., instabilities which require the presence of both magnetic field and shear flow. We show that a family of profiles originally studied by Tatsuno and Dorland remains unstable even when V'{sup 2}/4 < N {sup 2}, violating the Richardson criterion. However, not all magnetic fields can result in a violation of the Richardson criterion. We consider a class of flows originally considered by Kent, which are destabilized by a constant magnetic field, and show that they become stable when V'{sup 2}/4 < N {sup 2}, as predicted by the Richardson criterion. This suggests that magnetic free energy is required to violate the Richardson criterion. This work implies that the Richardson criterion cannot be used when evaluating the ideal stability of a sheared, stably stratified, and magnetized plasma. We briefly discuss the implications for astrophysical systems.
- OSTI ID:
- 21394194
- Journal Information:
- Astrophysical Journal, Vol. 712, Issue 2; Other Information: DOI: 10.1088/0004-637X/712/2/1116; ISSN 0004-637X
- Country of Publication:
- United States
- Language:
- English
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