On Stability of MHD flow around a cylinder in an aligned magnetic fields

The hydromagnetic stability of the flow of an incompressible conducting fluid around a circular cyliner in a uniform magnetic field parallel to the mean flow is investigated with different approaches:

Experiments for 1000 < Re < 9000
a simple analytical model
numerical simulation for Re < 1000.
Main goal of the investigations is to find the stability curce inthe (Re, N)-plane, and to distinguish between 2D and 3D instabilities.
Experimental results will be presented based on hot-wire measurements in the down-stream cylinder wake. The suppression of the vortex street by increasing magnetic fields is clearly identified.
Parallel to the disappearance of the typical Kármán frequency an increase of low frequency fluctuations is observed in the spectrum. This will be discussed in therms of theoretical predictions for long-wave MHD instabilities.
More physical insight into the stability behaviour is obtained by a simple Kolmogorov flow modelling of the cylinder wake and the corresponding stability analysis. Theoretical results will be presented for the 2D case: critical Reynolds number, wave number and Strouhal number as function of the magnetic field.
The critical wave number jumbs form the region of the typical Kármán value to very low values at a distinct magnetic field strength. The simple model is extended to include 3D instabilities in the flow. Limitations of the model and the comparison to experiments will be discussed.
Finally the 2D case for Re < 1000 will be compared with results of a full numerical simulation.