By methods of modern spectral analysis, we rigorously find distributions of eigenvalues of linearized operators associated with an ideal hydromagnetic Couette-Taylor flow. The transition to instability in the limit of a vanishing magnetic field has a discontinuous change compared to the Rayleigh stability criterion for hydrodynamical flows, which is known as the Velikhov-Chandrasekhar paradox.

This equation expresses U2 as the ratio of two positive definite integrals. Accordingly, the solution is stable; moreover, it can be shown that equation (25) providesthe basis for a variational method of determining u2. The explicit solution of the underlying problem in hydromagnetic oscillations in case the prevailing fields are axisymmetric has many interesting features. They will be discusse...

The stability of the hydromagnetic Couette flow is investigated when a constant current is applied along the axis of the cylinders. It is shown that if the resulting toroidal magnetic field depends only on this current, no linear instability to axisymmetric disturbances is possible. c © 2005 Elsevier Ltd. All rights reserved.

Magnetic dynamo experiments are being performed in many laboratories throughout the world. The most successful have been at Kalsruhe and Riga where liquid sodium has been forced in constrained flows and produced predicted postive dynamo gain. The unconstrained flows are being investigated at Wisconsin, Cadarache , and Maryland. These experiments have not reached the critical values of the magne...

Nonhelical hydromagnetic forced turbulence is investigated using large scale simulations on up to 256 processors and 1024(3) mesh points. The magnetic Prandtl number is varied between 1/8 and 30, although in most cases it is unity. When the magnetic Reynolds number is based on the inverse forcing wave number, the critical value for dynamo action is shown to be around 35 for magnetic Prandtl num...