Hydromagnetic instability of rotating pipe flow

Abstract

Stability characteristics of the flow of incompressible viscous fluid, subjected to a uniform magnetic field are investi- gated. The temporal evolution of infinitesimal perturbations is performed by spectral computation of Navier-Stokes equations. Unlike the linear stability of pipe flow at all Reynolds numbers, this study reports on its linear instability when the rotating system is subjected to a streamwise magnetic field. It is found that the small rotation and magnetic numbers exhibit some unstable modes for three-dimensional perturbations. In addition, the large rotation numbers help to stabilize the flow while the reverse nature is observed as the magnetic pressure number increase. It is also shown that the rightmost eigenvalues in the spectrum are waves propagating with a global speed equal to 2M .