Three-dimensional linear stability analysis of lid-driven MHD cavity flow

We present numerical results of a linear 3-D stability analysis of a square lid-driven cavity flow under the influence of an external magnetic field which is directed parallel to the lid. For Reynolds numbers up to Re * 7800 the 2-D hydrodynamic flow is steady. The Lorentz force has a strong influence on the 2-D flow structure, thereby changing number, shape and strength of the eddies inside. The resulting 3-D stability behaviour is rather complex since it depends on the 2-D flow structure. Although increasing magnetic fields are able to damp 3-D instability, in a parameter region around Re = 3100, several branches of the neutral stability curve do exist. This leads to a non-monotonic behaviour of receptivity to 3-D disturbances as the strength of the magnetic field is increased.