O.N. Kirillov, D.E. Pelinovsky, and G. Schneider

Paradoxical transitions to instabilities in hydromagnetic Couette-Taylor fows

Physical Review E 84, 065301(R) (4 pages) (2011)

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

instabilities of hydromagnetic flows, eigenvalues of linearized operators, quadratic eigenvalue problems.