| Type |
Journal Article |
| Names |
Daniel Lecoanet, Ellen G. Zweibel, Richard H. D. Townsend, Yi-Min Huang |
| Publication |
The Astrophysical Journal |
| Volume |
712 |
| Issue |
2 |
| Pages |
1116-1128 |
| Date |
April 1, 2010 |
| URL |
http://adsabs.harvard.edu/abs/2010ApJ...712.1116L |
| Library Catalog |
NASA ADS |
| Abstract |
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-Väisälä frequency N 2 if
V'2/4>N 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 & Dorland remains unstable
even when V'2/4 < N 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'2/4 < N
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. |
| Tags |
Instabilities, Magnetohydrodynamics: MHD, hydrodynamics, stars: magnetic field, stars: rotation |