On the nonlinear mechanics of magnetohydrodynamic stability

The nonlinear stability of magnetized plane Poiseuille flow, the magnetized plane jet, and the plane current-vortex sheet is examined. If it is assumed that the perturbation retains the form of the linearly unstable eigenmode, and that the most significant nonlinear effect is the distortion of the mean flow and magnetic field, then a Landau nonlinear stability equation can be derived from the streamwise-averaged perturbation energy balance. Secondary equilibrium velocity and magnetic fields are predicted. The possibility of subcritical instabilities also is discussed.