Violation of Richardson's Criterion via Introduction of a Magnetic Field

Details Violation of Richardson's Criterion via Introduction of a Magnetic Field Violation of Richardson's Criterion via Introduction of a Magnetic Field

2010-02-17

arxiv.org/abs/1002.3335v1

Astronomy and Astrophysics

Astrophysics

Solar and Stellar Astrophysics

Accepted to ApJ, 48 pages, 9 figures

Scientific paper

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-Vaisala 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 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 (2006) remain unstable even when $V'^2/4

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