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

Mutschke, G.; Gerbeth, G.; Shatrov, V.; Tomboulides, A.

A more detailed look is given on the scenario of 3-D instabilities taking place in the MHD cylinder flow when oncoming flow and magnetic field are parallel, thus extending our previous letter \cite{PHFL97}. The results presented here are in the frame of a linear stability analysis in the range 100 As the strength of the magnetic field is increased, a non-monotonic behaviour of 3-D instability is found. This is mainly due to the fact that the underlying 2-D flow changes considerably from periodic to steady flow while different instability mechanisms are superimposed. The behaviour at weak magnetic fields depends on the Reynolds number
and is either a damping or an enhancing influence on 3-D instability. At the critical value of 2-D instability $N_c^{2D}$
a local maximum in the 3-D instability curve occurs which leads to 3-D instability at Reynolds numbers down to $Re \sim 150$,
i.e.~lower than in the hydrodynamic cylinder flow. Increasing $N$ further, 3-D instability is first being damped while for larger values of the magnetic field 3-D instability is generally amplified. Therefore, 3-D steady flows at strong magnetic fields may also exist at Reynolds numbers which are considerably lower than the critical
Reynolds number for the onset of three-dimensionality of purely hydrodynamic cylinder flow.
For transverse magnetic fields, a mainly monotonic and much stronger damping of three-dimensionality as compared to the aligned field case is found when the strength of the magnetic field increases.

Keywords: Fluid dynamics; MHD; Flow Stability; Linear Stability Analysis

  • Physics of Fluids Vol 13, No 3, (March 2001) pp. 723-734

Permalink: https://www.hzdr.de/publications/Publ-3079
Publ.-Id: 3079