Linear and nonlinear stability in resistive magnetohydrodynamics
This document reports recent progress on the resistive or dissipative magnetohydrodynamics (MHD) in general geometry. A sufficient stability condition with respect to purely growing modes is derived for resistive magnetohydrodynamics. Its nearness to necessity is analysed and it is found that for physically reasonable approximations the condition is in some sense necessary and sufficient for stability against all modes. Physically motivated test functions are introduced. This leads to simplified versions of the stability functional, which makes its evaluation and minimisation more tractable. Nonlinear stability in hydrodynamics and magnetohydrodynamics is discussed, especially in connection with unconditional stability and with severe limitations on the Reynolds number. A special inertia-caused Hopf bifurcation is identified and the nature of the resulting attractors is also discussed.
Bibliographic Reference: Report: IPP 6/314 EN (1993) 18 pp.
Availability: Available from Max-Planck-Institut für Plasmaphysik, 8046 Garching bei München (DE)
Record Number: 199310652 / Last updated on: 1994-11-29
Original language: en
Available languages: en