The scenario of three-dimensional instabilities of the cylinder wake in an external magnetic field: A linear stability analysis

A more detailed look is given on the scenario of three-dimensional (3-D) instabilities in the magnetohydrodynamic cylinder flow when the oncoming flow and the magnetic field are parallel. The results presented here are in the frame of linear stability analysis in the range 100 < Re < 250 and extend the results in our previous letter [Phys. Fluids 9, 3114 (1997)]. As the strength of the magnetic field is increased, a nonmonotonic behavior of the 3-D instability is found. This is mainly due to the fact that the underlying two-dimensional (2-D) flow changes considerably from periodic to steady while different instability mechanisms are counteracting. The behavior at weak magnetic fields depends on the Reynolds number and has either a damping or an enhancing influence on 3-D instability. A local maximum is observed in the 3-D instability curve, close to the critical value for 2-D instability, N-c(2-D), leading to 3-D instability at Reynolds numbers as low as Re similar to 150, i.e., lower than the critical Reynolds number for the onset of three dimensionality, Re-c(3-D), in the pure hydrodynamic cylinder flow. By increasing the magnetic field strength further, the 3-D instability is first damped while for larger values of N it is generally amplified. Therefore, for strong magnetic fields, 3-D steady flows may exist at Re which are considerably lower than Re-c(3-D) of the pure hydrodynamic cylinder flow. In the case of a transverse magnetic field, a stronger and approximately monotonic damping of three dimensionality was observed with increasing magnetic field strength. (C) 2001 American Institute of Physics.