Linear and Nonlinear Stability in Resistive Magnetohydrodynamics

✍ Scribed by H. Tasso

• Publisher: Elsevier Science
• Year: 1994
• Tongue: English
• Weight: 530 KB
• Volume: 234
• Category: Article
• ISSN: 0003-4916
• DOI: 10.1006/aphy.1994.1079

✦ Synopsis

A sufficient stability condition with respect to purely growing modes is derived for resistive magnetohydrodynamics. Its "nearness" to necessity is analysed. It is found that for physically reasonable approximations the condition is in some sense necessary and sufficient for stability against all modes. This, together with hermiticity makes its analytical and numerical evaluation worthwhile for the optimization of magnetic configurations. Physically motivated test functions are introduced. This leads to simplified versions of the stability functional, which makes its evaluation and minimization more tractable. In the case of special force-free fields the simplified functional reduces to a good approximation of the exact stability functional derived by other means. It turns out that in this case the condition is also sufficient for nonlinear stability. Nonlinear stability in hydrodynamics and magnetohydrodynamics is discussed especially in connection with "unconditional" stability and with severe limitations on the Reynolds number. Two examples in magnetohydrodynamics show that the limitations on the Reynolds numbers can be removed but unconditional stability is preserved. Practical stability needs to be treated for limited levels of perturbations or for conditional stability. This implies some knowledge of the basin of attraction of the unperturbed solution, which is a very difficult problem. Finally, a special inertia-caused Hopf bifurcation is identified and the nature of the resulting attractors is discussed. 1994 Academic Press. Inc.