A contribution to the stability of electrically conducting Boussinesq fluids by the energy method

The energy method of Reynolds and Orr, for flows subject to finite disturbances, is extended to include approximate base flows and flows in which inertial and/or Lorentz forces of the base flow are of comparable or greater magnitude than the impressed body force field. The extension given is consistent with the well-known Boussinesq approximation. Two new stability criteria were established which demonstrate the effect of allowing approximate base flows. The universal stability boundary considers only the extremal characteristics of the base flow. The optimal stability boundary criteria applies variational techniques and utilizes more details of the base flow to obtain the largest possible stability region consistent with the theory. The theory is applied to the problem of heated Couette flow, both with and without internal viscous heating.