Magnetohydrodynamic (MHD) flows in annular channels are of great current interest due to experimental search for the so-called magnetorotational instability (MRI) which is important for astrophysical applications (accretion disk physics, magnetic dynamo effect). <p>The main point of MRI experiments is to study the stability of liquid metal rotating in an external magnetic field. Two different types of fluid rotation are proposed: Taylor-Couette flow between rotating coaxial cylinders and electrically driven flow in transverse magnetic field. The implementation of MRI experiments and explanation of experimental results requires a theoretical study of the equilibrium and the stability of MHD flow in an annular channel. This is one of the main tasks of present thesis.<p>For study of equilibrium Taylor-Couette and electrically driven flows, a numerical code is developed which is based on the finite difference scheme with Jacobi iterations. The structure of flows is calculated for different parameters of the experiment. Effect of the inertia on the rotation profiles is investigated in detail. The approximate analytical expressions are obtained for radial profiles of rotation that can be used for optimization of the experimental device for MRI investigation. Equilibrium Taylor-Couette and electrically driven flows are compared from the perspective of experimental studies of MRI.<p>The spectral stability of electrically driven flow is studied by solving the eigen-value problem. This study is performed in the frames of both ideal and dissipative MHD models. It is shown that electrically driven flow can be destabilized through the mechanism of MRI if fluid velocity exceeds some instability threshold, which is determined by non-axisymmetric modes. The obtained results are compared with available experimental data.<p>A general variational method is developed for the stability study of MHD flows of ideal compressible fluids. It is shown that the linearized dynamics of such fluids has an infinite set of invariants. A necessary and sufficient stability criterion can be obtained after inclusion of one or several such invariants in analysis. An analytical example is presented to confirm the fruitfulness of the developed method.

Magnetohydrodynamic (MHD) flows in annular channels are of great current interest due to experimental search for the so-called magnetorotational instability (MRI) which is important for astrophysical applications (accretion disk physics, magnetic dynamo effect). <p>The main point of MRI experiments is to study the stability of liquid metal rotating in an external magnetic field. Two different types of fluid rotation are proposed: Taylor-Couette flow between rotating coaxial cylinders and electrically driven flow in transverse magnetic field. The implementation of MRI experiments and explanation of experimental results requires a theoretical study of the equilibrium and the stability of MHD flow in an annular channel. This is one of the main tasks of present thesis.<p>For study of equilibrium Taylor-Couette and electrically driven flows, a numerical code is developed which is based on the finite difference scheme with Jacobi iterations. The structure of flows is calculated for different parameters of the experiment. Effect of the inertia on the rotation profiles is investigated in detail. The approximate analytical expressions are obtained for radial profiles of rotation that can be used for optimization of the experimental device for MRI investigation. Equilibrium Taylor-Couette and electrically driven flows are compared from the perspective of experimental studies of MRI.<p>The spectral stability of electrically driven flow is studied by solving the eigen-value problem. This study is performed in the frames of both ideal and dissipative MHD models. It is shown that electrically driven flow can be destabilized through the mechanism of MRI if fluid velocity exceeds some instability threshold, which is determined by non-axisymmetric modes. The obtained results are compared with available experimental data.<p>A general variational method is developed for the stability study of MHD flows of ideal compressible fluids. It is shown that the linearized dynamics of such fluids has an infinite set of invariants. A necessary and sufficient stability criterion can be obtained after inclusion of one or several such invariants in analysis. An analytical example is presented to confirm the fruitfulness of the developed method.