LINEAR AND NONLINEAR STABILITY OF HELICAL FLOW OF A HETEROGENEOUS CONDUCTING FLUID

TL;DRAbstract

The problem of linear and nonlinear stability of a helical flow of a perfectly conducting heterogeneous fluid between two coaxial cylinders in the presence of an azimuthal magnetic field and a radial gravitational force is discussed. In the case of linear stability the problem has been formulated by the normal mode method and the analysis has been carried out by reducing the perturbation equations to a Sturm-Liouville system. It is found that a necessary condition for instability is that the algebraic sum of hydrodynamic, magnetohydrodynamic and swirling Richardson numbers must be less than one quarter somewhere in the fluid. A semi-circle theorem similar to that of Howard is also obtained. In particular it is found that when gravitational force balances the centrifugal force of the swirling motion, the heterogeneous conducting fluid behaves as if it is homogeneous as far as the condition for stability is concerned. In the case of nonlinear stability the problem has been formulated by

Chat with Paper

AI Agents for this Paper