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

We present numerical results of a linear three-dimensional (3D) stability analysis of a square lid-driven cavity flow under the influence of an external magnetic field which is directed parallel to the lid. The Lorentz force has a strong influence on the two-dimensional (2D) flow structure, thereby changing number, shape and strength of the eddies. The resulting 3D stability behavior is rather complex since it depends on the 2D flow structure. Although increasing magnetic fields are able to damp 3D instability, in a parameter region around Re =3100, several branches of the neutral stability curve do exist. For a fixed Reynolds number in this range, an increase of the magnetic field strength may lead to a transition from a stable flow to an oscillatory unstable one.